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
Algebra
Matrices & Determinants
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
Problem 3 2 points Find a basis for Span 1 2x 2x x 1 x 1 x in V
Algebra
Matrices & Determinants
Problem 3 2 points Find a basis for Span 1 2x 2x x 1 x 1 x in V
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
Algebra
Matrices & Determinants
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
point Find two basic solutions to the following system of homogeneous equations x y 2z 4w 0 4x 2y z w 0
Algebra
Matrices & Determinants
point 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
Algebra
Matrices & Determinants
Which is a solution for 4x 8 3x 14 A 2 22 OB 2 7 C 3 D 6 O E 7
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
Algebra
Matrices & Determinants
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
Find all zeros of f x 8x 4 20x 3 10x 2 5x 3 stating multiplicity when appropriate
Algebra
Matrices & Determinants
Find 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
Algebra
Matrices & Determinants
b c a b c 1 2 0 12 1 3 1 7 122 3 3 4 5 L
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
Algebra
Matrices & Determinants
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
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
Algebra
Matrices & Determinants
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
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
Algebra
Matrices & Determinants
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
Find the equation in terms of x of the line through the points 1 7 and 2 2 Y Question Hol
Algebra
Matrices & Determinants
Find the equation in terms of x of the line through the points 1 7 and 2 2 Y Question Hol
36 6x 3x 2
Algebra
Matrices & Determinants
36 6x 3x 2
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
Algebra
Matrices & Determinants
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
Find the reduced row echelon form of this augmented matrix 1 2 0 150 1 1 3 200 0 0 1 250
Algebra
Matrices & Determinants
Find 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
Algebra
Matrices & Determinants
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
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
Algebra
Matrices & Determinants
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
Write the system of equations as an augmented matrix m c 100 250 a 150 C
Algebra
Matrices & Determinants
Write 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
Algebra
Matrices & Determinants
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
By locating the pivots find a basis for the column space of 0 5 4 3 0021 0000 00 U
Algebra
Matrices & Determinants
By 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
Algebra
Matrices & Determinants
8 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
Algebra
Matrices & Determinants
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
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
Algebra
Matrices & Determinants
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
3 Solve the systems 3x 4y 2z 15 2x 4y z 16 2x 3y 5z 20
Algebra
Matrices & Determinants
3 Solve the systems 3x 4y 2z 15 2x 4y z 16 2x 3y 5z 20
1 Solve the systems x y z 14 2y 3z 14 16y 24z 112
Algebra
Matrices & Determinants
1 Solve the systems x y z 14 2y 3z 14 16y 24z 112
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
Algebra
Matrices & Determinants
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
write an equation for the graph The equation for the graph is O A NONA O 6 4 2 2 4 6 2
Algebra
Matrices & Determinants
write 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
Algebra
Matrices & Determinants
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
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
Algebra
Matrices & Determinants
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
E 11 Given a vector A 3a 2a 16a find its components normal to the plane 2x 2yz 8 0 and tangential to it
Algebra
Matrices & Determinants
E 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
Algebra
Matrices & Determinants
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
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
Algebra
Matrices & Determinants
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
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
Algebra
Matrices & Determinants
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
Write the system of equations as an augmented matrix 2a 4c 4r 68 6a c 5T 48 7c 14 a 7r
Algebra
Matrices & Determinants
Write 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
Algebra
Matrices & Determinants
Write 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
Algebra
Matrices & Determinants
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
Let A and B 10 2 6 8 5 6 1 3 9 10 then use the matrices above to perform matrix multiplication AB
Algebra
Matrices & Determinants
Let 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
Algebra
Matrices & Determinants
4 2 45 2 1 2 T 2 3 33 5 T 11
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
Algebra
Matrices & Determinants
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
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
Algebra
Matrices & Determinants
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
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
Algebra
Matrices & Determinants
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
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
Algebra
Matrices & Determinants
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
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
Algebra
Matrices & Determinants
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
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
Algebra
Matrices & Determinants
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
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
Algebra
Matrices & Determinants
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
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
Algebra
Matrices & Determinants
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
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
Algebra
Matrices & Determinants
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
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
Algebra
Matrices & Determinants
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
7 Use the Remainder Theorem to evaluate f x 6x4 x3 15x 2x 7 at x 2
Algebra
Matrices & Determinants
7 Use the Remainder Theorem to evaluate f x 6x4 x3 15x 2x 7 at x 2
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
Algebra
Matrices & Determinants
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