Matrices & Determinants Questions and Answers
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
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
Algebra
Matrices & Determinantspoint Find two basic solutions to the following system of homogeneous equations x y 2z 4w 0 4x 2y z w 0
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
Algebra
Matrices & DeterminantsFind all zeros of f x 8x 4 20x 3 10x 2 5x 3 stating multiplicity when appropriate
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
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
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
Algebra
Matrices & DeterminantsFind the equation in terms of x of the line through the points 1 7 and 2 2 Y Question Hol
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
Algebra
Matrices & DeterminantsFind the reduced row echelon form of this augmented matrix 1 2 0 150 1 1 3 200 0 0 1 250
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
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
Algebra
Matrices & DeterminantsWrite the system of equations as an augmented matrix m c 100 250 a 150 C
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
Algebra
Matrices & DeterminantsBy locating the pivots find a basis for the column space of 0 5 4 3 0021 0000 00 U
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
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
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
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
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
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
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
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
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
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
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
Algebra
Matrices & DeterminantsWrite the system of equations as an augmented matrix 2a 4c 4r 68 6a c 5T 48 7c 14 a 7r
Algebra
Matrices & DeterminantsWrite the system of equations as an augmented matrix 24 3c 300 100 350 2u y 9c C
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
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
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
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
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
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
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
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
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
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
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
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
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