Matrices & Determinants Questions and Answers
![Use mathematical induction on integer n to prove each of the following statements 7 c 1 3 4 1 2n 23n n 12 5 2n 1 1 4n for m 1](https://media.kunduz.com/media/sug-question-candidate/20230204043213334396-5360022.jpg?w=256)
Algebra
Matrices & DeterminantsUse mathematical induction on integer n to prove each of the following statements 7 c 1 3 4 1 2n 23n n 12 5 2n 1 1 4n for m 1
![Problem 3 2 points Find a basis for Span 1 2x 2x x 1 x 1 x in V](https://media.kunduz.com/media/sug-question-candidate/20230204031902010907-5359061.jpg?w=256)
![Find the unique n 1 th degree polynomials that pass through the given sets of n data points The data points 1 0 0 1 1 2 2 3](https://media.kunduz.com/media/sug-question-candidate/20230204041604852822-5357745.jpg?w=256)
Algebra
Matrices & DeterminantsFind the unique n 1 th degree polynomials that pass through the given sets of n data points The data points 1 0 0 1 1 2 2 3
![point Find two basic solutions to the following system of homogeneous equations x y 2z 4w 0 4x 2y z w 0](https://media.kunduz.com/media/sug-question-candidate/20230203225632472662-5359019.jpg?w=256)
Algebra
Matrices & Determinantspoint Find two basic solutions to the following system of homogeneous equations x y 2z 4w 0 4x 2y z w 0
![Which is a solution for 4x 8 3x 14 A 2 22 OB 2 7 C 3 D 6 O E 7](https://media.kunduz.com/media/sug-question-candidate/20230203203238184903-3739212.jpg?w=256)
![10 marks 1 Given the linear system x 2y 3z 1 2x By z 1 3x y 2z Find the values of a and B if any such that the system a has one single solution and give the solution values of x y z b has infinite solutions and give the solution values of x y z c has no solutions Verify your answers](https://media.kunduz.com/media/sug-question-candidate/20230203164747322232-5359148.jpg?w=256)
Algebra
Matrices & Determinants10 marks 1 Given the linear system x 2y 3z 1 2x By z 1 3x y 2z Find the values of a and B if any such that the system a has one single solution and give the solution values of x y z b has infinite solutions and give the solution values of x y z c has no solutions Verify your answers
![Find all zeros of f x 8x 4 20x 3 10x 2 5x 3 stating multiplicity when appropriate](https://media.kunduz.com/media/sug-question-candidate/20230203160041633178-5359003.jpg?w=256)
Algebra
Matrices & DeterminantsFind all zeros of f x 8x 4 20x 3 10x 2 5x 3 stating multiplicity when appropriate
![b c a b c 1 2 0 12 1 3 1 7 122 3 3 4 5 L](https://media.kunduz.com/media/sug-question-candidate/20230203130142528751-5358511.jpg?w=256)
![Let D 1 2 N and D 2 YN two sets data such that 3x 29 11 Yi 1 If MAD 12 find MAD2 2 If If MAD 12 find MAD2 3 If o 22 find o 4 If If o2 16 find o for all i 1 N 1](https://media.kunduz.com/media/sug-question-candidate/20230203092757941713-5357991.jpg?w=256)
Algebra
Matrices & DeterminantsLet D 1 2 N and D 2 YN two sets data such that 3x 29 11 Yi 1 If MAD 12 find MAD2 2 If If MAD 12 find MAD2 3 If o 22 find o 4 If If o2 16 find o for all i 1 N 1
![c What do you understand by the term LU decomposition Write the matrix below in the form A LU 1 5 3 2 1 1 1 where A 0 4 7 Marks](https://media.kunduz.com/media/sug-question-candidate/20230203070331315280-5357641.jpg?w=256)
Algebra
Matrices & Determinantsc What do you understand by the term LU decomposition Write the matrix below in the form A LU 1 5 3 2 1 1 1 where A 0 4 7 Marks
![Solve the following inequality Write the solution set using interval notation Express all values as integers or reduced fractions Enter DNE if no solution exists 1 5 5z 2 3](https://media.kunduz.com/media/sug-question-candidate/20230203040620602804-4492553.jpg?w=256)
Algebra
Matrices & DeterminantsSolve the following inequality Write the solution set using interval notation Express all values as integers or reduced fractions Enter DNE if no solution exists 1 5 5z 2 3
![Find the equation in terms of x of the line through the points 1 7 and 2 2 Y Question Hol](https://media.kunduz.com/media/sug-question-candidate/20230203030656178247-4492553.jpg?w=256)
Algebra
Matrices & DeterminantsFind the equation in terms of x of the line through the points 1 7 and 2 2 Y Question Hol
![36 6x 3x 2](https://media.kunduz.com/media/sug-question-candidate/20230203013551361606-5357340.jpg?w=256)
![Graph the line passing through 5 3 with slope m 4 14 12 10 8 6 4 2 14 12 10 8 64 2 24 8 10 12 14 246 8 10 12 14](https://media.kunduz.com/media/sug-question-candidate/20230203004814357144-5324074.jpg?w=256)
Algebra
Matrices & DeterminantsGraph the line passing through 5 3 with slope m 4 14 12 10 8 6 4 2 14 12 10 8 64 2 24 8 10 12 14 246 8 10 12 14
![Find the reduced row echelon form of this augmented matrix 1 2 0 150 1 1 3 200 0 0 1 250](https://media.kunduz.com/media/sug-question-candidate/20230203003034877403-4492553.jpg?w=256)
Algebra
Matrices & DeterminantsFind the reduced row echelon form of this augmented matrix 1 2 0 150 1 1 3 200 0 0 1 250
![Write the system of equations as an augmented matrix Then use the Gauss Jordan method to solve for x and y x 5y 3 2x 3y 1 Solution Enter the solution as an ordered nair y y with no r](https://media.kunduz.com/media/sug-question-candidate/20230203003124853343-4492553.jpg?w=256)
Algebra
Matrices & DeterminantsWrite the system of equations as an augmented matrix Then use the Gauss Jordan method to solve for x and y x 5y 3 2x 3y 1 Solution Enter the solution as an ordered nair y y with no r
![The given matrix is an augmented matrix representing a system of linear equations Use the Gauss Jordon elimination method to find the solution of the system 7 6 5 01 4 06 4 100 01 0 001 56 1 26](https://media.kunduz.com/media/sug-question-candidate/20230203003053993394-4492553.jpg?w=256)
Algebra
Matrices & DeterminantsThe given matrix is an augmented matrix representing a system of linear equations Use the Gauss Jordon elimination method to find the solution of the system 7 6 5 01 4 06 4 100 01 0 001 56 1 26
![Write the system of equations as an augmented matrix m c 100 250 a 150 C](https://media.kunduz.com/media/sug-question-candidate/20230203003018775734-4492553.jpg?w=256)
Algebra
Matrices & DeterminantsWrite the system of equations as an augmented matrix m c 100 250 a 150 C
![Convert to Scalar Form Determine how and intersect x 1 4s T y 5 6s 6t and 3x 2y 4z 17 0 1 z 1 3t](https://media.kunduz.com/media/sug-question-candidate/20230202201656203160-5357027.jpg?w=256)
Algebra
Matrices & DeterminantsConvert to Scalar Form Determine how and intersect x 1 4s T y 5 6s 6t and 3x 2y 4z 17 0 1 z 1 3t
![By locating the pivots find a basis for the column space of 0 5 4 3 0021 0000 00 U](https://media.kunduz.com/media/sug-question-candidate/20230202064046359538-5355709.jpg?w=256)
Algebra
Matrices & DeterminantsBy locating the pivots find a basis for the column space of 0 5 4 3 0021 0000 00 U
![8 Given a b 0 show that the matrix B a 0 88 b has operator norm a Compute its Hilbert Schmidt norm](https://media.kunduz.com/media/sug-question-candidate/20230202010416113863-5355377.jpg?w=256)
Algebra
Matrices & Determinants8 Given a b 0 show that the matrix B a 0 88 b has operator norm a Compute its Hilbert Schmidt norm
![7 Identify the singularities of 2 1 z 22 x 2 z and find the Laurent series for this function for each distinct annular region In each region gi general formulas for the series coefficients an bn](https://media.kunduz.com/media/sug-question-candidate/20230201050402060988-5349195.jpg?w=256)
Algebra
Matrices & Determinants7 Identify the singularities of 2 1 z 22 x 2 z and find the Laurent series for this function for each distinct annular region In each region gi general formulas for the series coefficients an bn
![11 Admission tickets to the Braden River Little League all star game cost 4 00 for adults and 1 50 for children A total of 225 tickets were sold and a total of 500 was collected from ticket sale How many adult tickets and how many children s tickets were sold Set up a system of equations an solve](https://media.kunduz.com/media/sug-question-candidate/20230201052502079252-4492553.jpg?w=256)
Algebra
Matrices & Determinants11 Admission tickets to the Braden River Little League all star game cost 4 00 for adults and 1 50 for children A total of 225 tickets were sold and a total of 500 was collected from ticket sale How many adult tickets and how many children s tickets were sold Set up a system of equations an solve
![3 Solve the systems 3x 4y 2z 15 2x 4y z 16 2x 3y 5z 20](https://media.kunduz.com/media/sug-question-candidate/20230201051723931267-4492553.jpg?w=256)
![1 Solve the systems x y z 14 2y 3z 14 16y 24z 112](https://media.kunduz.com/media/sug-question-candidate/20230201051743002074-4492553.jpg?w=256)
![1 point Let T be an linear transformation from R to Rs Let A be the matrix associated to T fill in the correct answer for each of the following situations 1 Two columns in the row echelon form of A are not pivot columns 2 The row echelon form of A has no column corresponding to a free variable 3 The row echelon form of A has a column corresponding to a free variable 4 Every column in the row echelon form of A is a pivot column A T is not one to one B T is one to one](https://media.kunduz.com/media/sug-question-candidate/20230201045112974881-5352772.jpg?w=256)
Algebra
Matrices & Determinants1 point Let T be an linear transformation from R to Rs Let A be the matrix associated to T fill in the correct answer for each of the following situations 1 Two columns in the row echelon form of A are not pivot columns 2 The row echelon form of A has no column corresponding to a free variable 3 The row echelon form of A has a column corresponding to a free variable 4 Every column in the row echelon form of A is a pivot column A T is not one to one B T is one to one
![write an equation for the graph The equation for the graph is O A NONA O 6 4 2 2 4 6 2](https://media.kunduz.com/media/sug-question-candidate/20230201022513560883-5353299.jpg?w=256)
Algebra
Matrices & Determinantswrite an equation for the graph The equation for the graph is O A NONA O 6 4 2 2 4 6 2
![2 Which of the following sets of vectors are independent i 2 2 3 2 2 4 4 4 6 ii 2 2 3 2 2 4 6 6 11 iii 2 2 3 2 2 4 10 10 17 A ii only B iii only C i only D i and iii only E i and ii only F ii and iii G all of them H none of them](https://media.kunduz.com/media/sug-question-candidate/20230201021437824027-5353311.jpg?w=256)
Algebra
Matrices & Determinants2 Which of the following sets of vectors are independent i 2 2 3 2 2 4 4 4 6 ii 2 2 3 2 2 4 6 6 11 iii 2 2 3 2 2 4 10 10 17 A ii only B iii only C i only D i and iii only E i and ii only F ii and iii G all of them H none of them
![For the function g x 42 3 evaluate and simplify a g 9 4g 3 b g x 8 4x 29 c g x g 8 0 o](https://media.kunduz.com/media/sug-question-candidate/20230201002521689387-5324074.jpg?w=256)
Algebra
Matrices & DeterminantsFor the function g x 42 3 evaluate and simplify a g 9 4g 3 b g x 8 4x 29 c g x g 8 0 o
![E 11 Given a vector A 3a 2a 16a find its components normal to the plane 2x 2yz 8 0 and tangential to it](https://media.kunduz.com/media/sug-question-candidate/20230131070207406682-5350753.jpg?w=256)
Algebra
Matrices & DeterminantsE 11 Given a vector A 3a 2a 16a find its components normal to the plane 2x 2yz 8 0 and tangential to it
![Find the focus directrix vertex and axis of symmetry for the parabola 12 y 2 z 1 Focus 1 1 Directrix y 5 Vertex 1 2 Be sure to enter each answer in the appropriate format Hint What is the appropriate notation for a line or a point Graph the parabola Include the directrix and focus with your graph 63 43 2 L r 9 54 4 3 23 1 7737 2 2 A 45 6](https://media.kunduz.com/media/sug-question-candidate/20230131053140105011-4492553.jpg?w=256)
Algebra
Matrices & DeterminantsFind the focus directrix vertex and axis of symmetry for the parabola 12 y 2 z 1 Focus 1 1 Directrix y 5 Vertex 1 2 Be sure to enter each answer in the appropriate format Hint What is the appropriate notation for a line or a point Graph the parabola Include the directrix and focus with your graph 63 43 2 L r 9 54 4 3 23 1 7737 2 2 A 45 6
![The island arc running from the Virgin Islands to Trinidad and Tobago is called O The guianas O The Lesser Antilles The Bahamas O The Greater Antilles](https://media.kunduz.com/media/sug-question-candidate/20230131034922222555-4356528.jpg?w=256)
Algebra
Matrices & DeterminantsThe island arc running from the Virgin Islands to Trinidad and Tobago is called O The guianas O The Lesser Antilles The Bahamas O The Greater Antilles
![1 Given and 1 3 1 0 find AB and BA 3 AB BA 2 Hint Matrices need to be entered as elements of row 1 separated by commas elements of row 2 separated by commas elements of each row separated by commas Example C 1 2 3 3 would be entered as 1 2 3 4 5 6 4 5 6](https://media.kunduz.com/media/sug-question-candidate/20230131013803689223-4492553.jpg?w=256)
Algebra
Matrices & Determinants1 Given and 1 3 1 0 find AB and BA 3 AB BA 2 Hint Matrices need to be entered as elements of row 1 separated by commas elements of row 2 separated by commas elements of each row separated by commas Example C 1 2 3 3 would be entered as 1 2 3 4 5 6 4 5 6
![Write the system of equations as an augmented matrix 2a 4c 4r 68 6a c 5T 48 7c 14 a 7r](https://media.kunduz.com/media/sug-question-candidate/20230131015850461897-4492553.jpg?w=256)
Algebra
Matrices & DeterminantsWrite the system of equations as an augmented matrix 2a 4c 4r 68 6a c 5T 48 7c 14 a 7r
![Write the system of equations as an augmented matrix 24 3c 300 100 350 2u y 9c C](https://media.kunduz.com/media/sug-question-candidate/20230131015800901259-4492553.jpg?w=256)
Algebra
Matrices & DeterminantsWrite the system of equations as an augmented matrix 24 3c 300 100 350 2u y 9c C
![Given the matrices A A It is Select an answer Select an answer B If ad possible not possible 5 3 4 3 2 1 3 4 5 to add these matrices at is A B and B 2 5 4 5 4 2 1 5 4](https://media.kunduz.com/media/sug-question-candidate/20230131014104847328-4492553.jpg?w=256)
Algebra
Matrices & DeterminantsGiven the matrices A A It is Select an answer Select an answer B If ad possible not possible 5 3 4 3 2 1 3 4 5 to add these matrices at is A B and B 2 5 4 5 4 2 1 5 4
![Let A and B 10 2 6 8 5 6 1 3 9 10 then use the matrices above to perform matrix multiplication AB](https://media.kunduz.com/media/sug-question-candidate/20230131013730148529-4492553.jpg?w=256)
Algebra
Matrices & DeterminantsLet A and B 10 2 6 8 5 6 1 3 9 10 then use the matrices above to perform matrix multiplication AB
![4 2 45 2 1 2 T 2 3 33 5 T 11](https://media.kunduz.com/media/sug-question-candidate/20230131013712383078-4492553.jpg?w=256)
![Matrix A has the dimensions 3 x 6 and Matrix B has the dimensions 6 x 4 What are the dimensions of the product AB X note if multiplication is not possible put 1 in for both the row column dimensions](https://media.kunduz.com/media/sug-question-candidate/20230131013645684939-4492553.jpg?w=256)
Algebra
Matrices & DeterminantsMatrix A has the dimensions 3 x 6 and Matrix B has the dimensions 6 x 4 What are the dimensions of the product AB X note if multiplication is not possible put 1 in for both the row column dimensions
![Find the roots of the following quadratic equa tions by factoring 7 x 2x 1 0 8 x 8x 15 0 9 x 1 0 10 x 6x 8 0 11 x 4x 21 0 12 x 4x 12 0 13 x 10x 24 0 14 x2 11x 24 0 15 x 4x 5 0 16 x 10x 24 0](https://media.kunduz.com/media/sug-question-candidate/20230131002055836331-4140114.jpg?w=256)
Algebra
Matrices & DeterminantsFind the roots of the following quadratic equa tions by factoring 7 x 2x 1 0 8 x 8x 15 0 9 x 1 0 10 x 6x 8 0 11 x 4x 21 0 12 x 4x 12 0 13 x 10x 24 0 14 x2 11x 24 0 15 x 4x 5 0 16 x 10x 24 0
![Decide if the following statements are true 1 y 2 is a root of y y 6 0 2 x 1 and x 3 are roots of x 4x 3 0 3 x 2 and x 6 are roots of x 4x 12 0 4 y 1 and y 3 4 are roots of 4y 7y 3 0 5 x 1 and x 2 3 are roots of 3x 5x 2 0](https://media.kunduz.com/media/sug-question-candidate/20230131002011181541-4140114.jpg?w=256)
Algebra
Matrices & DeterminantsDecide if the following statements are true 1 y 2 is a root of y y 6 0 2 x 1 and x 3 are roots of x 4x 3 0 3 x 2 and x 6 are roots of x 4x 12 0 4 y 1 and y 3 4 are roots of 4y 7y 3 0 5 x 1 and x 2 3 are roots of 3x 5x 2 0
![Given the system of equations 2x 3y 9z 15 1 3z 3 3x y 4z 2 a Determine the type of system inconsistent dependent o b If your answer is dependent in a find the complete solution Write x y as functions of t where z t If your answer is inconsistent write DNE for all three variables 49 I y 11](https://media.kunduz.com/media/sug-question-candidate/20230130235319244291-4492553.jpg?w=256)
Algebra
Matrices & DeterminantsGiven the system of equations 2x 3y 9z 15 1 3z 3 3x y 4z 2 a Determine the type of system inconsistent dependent o b If your answer is dependent in a find the complete solution Write x y as functions of t where z t If your answer is inconsistent write DNE for all three variables 49 I y 11
![1 3 marks Find a formula for the nth term of the sequence defined by the third order recursion tn 3 7tn 1 6tn with initial values to 2 t 8 t 0 Calculate t3 directly and use it to check your formula n 0 1 2 3 tn 2 8 0](https://media.kunduz.com/media/sug-question-candidate/20230130232115615104-4665931.jpg?w=256)
Algebra
Matrices & Determinants1 3 marks Find a formula for the nth term of the sequence defined by the third order recursion tn 3 7tn 1 6tn with initial values to 2 t 8 t 0 Calculate t3 directly and use it to check your formula n 0 1 2 3 tn 2 8 0
![Ricardo invests 4100 in two different accounts The first account paid 8 the second account paid 5 in interest At the end of the first year he had earned 292 in interest How much was in each account s at 8 at 5](https://media.kunduz.com/media/sug-question-candidate/20230130230235825577-4492553.jpg?w=256)
Algebra
Matrices & DeterminantsRicardo invests 4100 in two different accounts The first account paid 8 the second account paid 5 in interest At the end of the first year he had earned 292 in interest How much was in each account s at 8 at 5
![The shape of this graph is best described as symmetric skewed constant peaks and valleys 12 10 8 6 4 2 CO 666 0 100 199 2012 Housing Prices 200 299 300 399 400 499 500 599 600 699 IL 700 799 668 008 Sales Price Thousands of Dollars](https://media.kunduz.com/media/sug-question-candidate/20230130220154772935-4491561.jpg?w=256)
Algebra
Matrices & DeterminantsThe shape of this graph is best described as symmetric skewed constant peaks and valleys 12 10 8 6 4 2 CO 666 0 100 199 2012 Housing Prices 200 299 300 399 400 499 500 599 600 699 IL 700 799 668 008 Sales Price Thousands of Dollars
![5 Let a b E R and define a matrix by a 1 T E b a Is T necessarily invertible Explain your reasoning b Show that for all a b R T has two distinct real eigenvalues c Now suppose a b Find an eigenvector for each eigenvalue of 7](https://media.kunduz.com/media/sug-question-candidate/20230130090603445367-5348279.jpg?w=256)
Algebra
Matrices & Determinants5 Let a b E R and define a matrix by a 1 T E b a Is T necessarily invertible Explain your reasoning b Show that for all a b R T has two distinct real eigenvalues c Now suppose a b Find an eigenvector for each eigenvalue of 7
![Determine the scalar equation i e standard form of the plane with vector equation 16 0 0 0 5 s 2 t 3 2 5](https://media.kunduz.com/media/sug-question-candidate/20230130043116851260-5347809.jpg?w=256)
Algebra
Matrices & DeterminantsDetermine the scalar equation i e standard form of the plane with vector equation 16 0 0 0 5 s 2 t 3 2 5
![Pivot the matrix about the circled element 26 0 4 3 0 2 13 The result of pivoting is Type an integer or simplified fraction for each matrix elemen on for each Pivot the matrix about the circled element 2542 1 58 4024 The result of pivoting is Type an integer or simplified fraction for each matrix element](https://media.kunduz.com/media/sug-question-candidate/20230130030224821949-5347809.jpg?w=256)
Algebra
Matrices & DeterminantsPivot the matrix about the circled element 26 0 4 3 0 2 13 The result of pivoting is Type an integer or simplified fraction for each matrix elemen on for each Pivot the matrix about the circled element 2542 1 58 4024 The result of pivoting is Type an integer or simplified fraction for each matrix element
![7 Use the Remainder Theorem to evaluate f x 6x4 x3 15x 2x 7 at x 2](https://media.kunduz.com/media/sug-question-candidate/20230130020838873634-4492553.jpg?w=256)
![Find a basis and the dimension of the solution space of the homogeneous system 2x2 x3 2x4 x5 0 1 2x2 2x3 x4 0 x1 4x2 x3 2x4 x5 0](https://media.kunduz.com/media/sug-question-candidate/20230129192128051857-5347386.jpg?w=256)
Algebra
Matrices & DeterminantsFind a basis and the dimension of the solution space of the homogeneous system 2x2 x3 2x4 x5 0 1 2x2 2x3 x4 0 x1 4x2 x3 2x4 x5 0