Matrices & Determinants Questions and Answers

Let S be the tetrahedron in R3 with vertices at X3 the vectors 0 0 02 and e3 and let S be the tetrahedron with vertices at vectors 0 V V and v3 See the figures to the right Complete parts a and b below a Describe a linear transformation that maps S onto S If T is a linear transformation that maps S onto S then the standard matrix for T written in terms of V V and V3 is A 1 b Find a formula for the volume of the tetrahedron S using the fact that volume of S 3 A 1 O C 1 2 det v det V V V3 det V V V3 area of base height OB det V V V3 V2 OD 1 det V V V3

2 Find the sum of the determinants 32 14 1 7 3 2 O 10 O 13 O 3 None of these choices are correct 0 7

Solve the matrix equation O O 10 l 13 5 10 13 5 51 51 1 14 5 1 4 5 5 4 None of these choices are correct 5 21 51 5 5 21 4 5 5 4 71x16 21 12 2 2 4 3

Solve X AX F where A 221 7 1 F 2 3 2 2 10t and X 0 3

Solve the following system by finding the determinants and using Cramer s Rule 2x y 4 and 3x y 1 O D 3 Dx 3 Dy 6 Answer 1 2 D 5 Dx 5 Dy 10 Answer 1 2 None of these choices are correct D 2 Dx 2 Dy 4 Answer 1 2 D 10 Dx 10 Dy 20 Answer 1 2

Solve the matrix equation 7 2y 4 121 23 2321 21 x 32 71 1 3 3zl 1 3zl 7w 5 O x 1 y 2 z 1 w 2 x 8 y 2 z 1 w 3 O x 3 y 6 z 0 w 3 O x 4 y 6 z 0 w 2 O None of these choices are correct

Sketch a graph of 7 6 5 4 3 2 x 1 1 7 6 5 A 32 3 2 2 3 4 5 6 74 y 3 1 4 1 2 3 4 5 6 7

This matrix repi shoes for the Men s and Women s departments of a clothing store If the salesperson gets 11 commission how much of each category was paid to the salesperson 1300 14001 Sales 2000 1800 1600 1200 143 00 154 00 o 220 00 198 00 176 00 132 00 1430 00 1540 00 2200 00 1980 00 1760 00 1320 00 14300 15400 22000 19800 17600 13200 None of these choices are correct 14 30 15 401 22 00 19 80 17 60 13 20

7 Shawna borrows 17 650 at an interest rate of 7 8 compounded monthly to pay for a new car Shawna plans to repay the loan monthly over the next 4 years When Shawna s loan is paid in full how much will she have actually paid for the car N 1 PV PMT FV P Y C Y

Four pounds of tea and 5 pounds of coffee cost 88 30 while 9 pounds of tea and six pounds of coffee cost 144 60 What is the cost of each per pound Cost of 1 pound of tea 9 20 and cost of 1 pound of coffee 10 30 Cost of 1 pound of tea 4 78 and cost of 1 pound of coffee 12 88 O Cost of 1 pound of tea 8 20 and cost of 1 pound of coffee 10 30

Question 51 Points 1 Identify the linear inequality from the following O4a 5b 9 O 4x 5y 9 O 4a 5b 9 3c

Find the vector x determined by the given coordinate vector x and the given basis B B 1 5 0 2 2 6 3 7 4 x B 4 8 2

Given that A 5 8 331 and B 2 17 12 determine the followin 4

M 26 33 23 6 8 14 19 16 3 20 20 20 14 30 1 13 Factorize M PDP where D is a block diago matrix

Show that the columns of O are orthogonal using ar appropriate matrix operation State the operation Indicate O 11 6 3 1 362325 3263 6 3 2 1 3 1 6 1 1 6 3 2 6 1 2 6 3 3236 2 3 21

Show that the columns of O are orthogonal using an appropriate matrix operation State the operation Indicate O 6 3 1 3263 6 1 1 3 3 6 3 6 2 1 2 3 6 3 6 2 1 3 2

Apply gram schmidt orthogonalization process to construct an orthonormal basis for W spanned by x1 x2 X3 where 2 2 2 1 x1 2 2 1 2 1 x x

Of the choices below only 069 99 23 46 35 39 39 89 02 917111 is not row equivalent to the matric 35 46

Find the perimeter of quadrilateral LMNO 10 9 8 7 6 5 4 3 2 104 L O 57 6549LB6 8 7 3 1 2 3 4 5 6 7 M N 1 2 3 4 5 6 7 8 9 10

1 3 Suppose A a 1 value of a 2 11 a 2 1 cannot be diagonalized please find the

6 Simplify the matrices Remember the order of operations 3 6 5 6 4 1 0 6 4 1 3 1 351 OPL

Which of the following sets is linearly independent in P 1 2x 5x 2 4x O the above set O None of the mentioned

Let W d a 5c 0 be a subspace of M2 2 C Then dimension of W is equal to 4 2 O 3 01 None of the mentioned Let m be a real number and M 2 9 3 6 If M is a linearly dependent set of M 2 then m 1 m 6 None of the mentioned

ind the product of the following two matrices 3 4 J 51 5 2 1

Starting with h 0 5 Find the next step size h in adaptive RK23 if the tolerance is 1 0 001 2 0 02 y y t y 0 2 y 1 t 3e 0 t 1

QUESTION 1 For the given matrices A B C and D below find if possible scalars r and s satisfying equations i and ii i AB rB ii CD sD A 6 1 1 0 0 13 16 8 11 13 5 B 27 0 13 5 6 70 6 00 7 20 2 40 4 10 2 40 7 20 4 80 7 70

For the matrix below decide whether the matrix has one solution no solution or infinitely many solutions If the matrix has one solution find it If the matrix has infinitely many solutions express your solution in terms of t where x x t y y t and z t 1 0 Lo 0 3 41 1 6 7 0 0 0 x y z 4 7 0 No solution x y z 4 3t 7 6t t

Perform the elementary row operation 45 2 531 15 Resulting matrix 1 18 RR on the given matrix Write numbers as integers or simplified fractions

lve the following system of linear equations 28 Ex1 4x2 4x3 x1 6x2 5x3 37 he system has infinitely many solutions select The system has at least one solution Your answer may use expressions involving the parameters r me system has at least one solution 1 0 2 0

Consider the following Universal Product Code 5 9 8 8 7 1 4 7 1 6 3 d Use the check vector c 3 1 3 1 3 1 3 1 3 1 3 1 to find c u in Z10 Find the check digit d d 5 9 8 8 7 1 4 7 1 6 3 d

Which of the following variables is appropriate for using a goodness of fit test one categorical variable and a sample drawn from a population with a known distribution Otwo categorical variables and a sample drawn from a population with a known distribution one categorical variable from two different populations O two categorical variables from two different populations

Find the distance between the pair of points 2 4 and 3 3 The exact distance is 74 units Type an exact answer using radicals as needed The distance is approximately units Round to the nearest thousandth as needed CUB

Given The data points 2 2 1 5 0 5 1 3 2 7 Suppose the errors in measuring the y values of the last two data points are greater than for the other points Weight these data points twice as much as the rest of the data 1 2 1 1 1 1 30 1 0 B 1 2 Weight B B y 25537 OA y 3 9 0 57x B y 7 9 1 87x OC y 4 0 0 93x

Find the distance between the pair of points 12 7 and 5 1 The exact distance is units Type an exact answer using radicals as needed COR

Determine whether the set B is a basis for the vector space V 14 V M22 B OB is a basis for V OB is not a basis for V 10 01 1 1 1 1 1 1 1 1

Given matrices 2 5 1 5 2 79 B 1 0 4 4 D 2 3 4 1 2 1 3 Compute the following 3A B a c d A CT D BT T

Find eigenvalues and eigenvectors of a matrix A where A 1 1 122 1

a Rewrite the angle as a sum or difference of special angles of your choice from the Unit Circle There are many correct ways to do this but do not yet find the value 15 b Now use the sum difference Identities to find the exact value Do not use decimal approximations sin 15

Find the area enclosed between the curve y and the x axis bound by the lines x and x 2

Solve the system of first order linear differential equations Use C and C as constants Y 1 3y2 V2 3y V 2 V1 t t ce 21 4t c ec e 21 4t

Let T be the linear opertor on R 3 which is represented by the matrix 3 1 22 1 2 2 0 What is diagonalizable operator D on R 3 and nilpotent operator N on R 3 s t T D N and DN ND

For which value of k does the matrix have one real eigenvalue of multiplicity 2 k A 6 58

Determine the minor of a22 in the matrix Answer How to enter your answer opens in new window 1 3 7 6 3 0 4 1 A 4

Answer How to enter your answer opens in new window A 2 4 6 93 3 1 L7 5 3

Evaluate the determinant of the matrix A 0 w 00 w3 0 0 0 W4 along and use the properties of determinants to simplify the process W4 Answer WS Minimize the required number of computations by carefully choosing a row or column to ex Ke Keyboard She

Graphing Practice 123 10 ft 3 ft The radius of this Ferris wheel is 10 feet and the bottom of the Ferris wheel is 3 feet above the ground The amount of time the Ferris wheel takes to make a complete revolution is 100 seconds When Evelyn gets on the Ferris wheel she is exactly 3 feet above the ground Then 50 seconds after starting she will be 23 feet above the ground at the peak of the Ferris wheel Then 100 seconds after starting she will be back to her starting position again exactly 3 feet above the ground 1 Write the function sine or cosine that models the scenario described above 2 Graph the function you created in 1 on the grid provided below 3 To the nearest tenth How high above the ground will Evelyn be after 43 seconds 4 To the nearest tenth when will Evelyn be 18 feet above the ground

Determine values of the variables that will make the following equation true if possible If not state Not Possible Answer How to enter your answer opens in new window 3 r 4 Selecting a checkbox will replace the entered answer value s with the checkbox value If the checkbox is not selected the entered a 27 Not Possible

Answer A 4 2 2 2 10 6 Selecting a checkbox will replace the entered answer value s with the checkbox value If the checkbox is not selected the ente Not Possible

6 Match the equation with Its given period 27 4 cos x 6 3 4 cos z 3 4 sin 2 3m 4 sin 67 DRAG DROP THE ANSWEE 4 6 3x 6 3

Answer A 4 2023 Hawkes Learning B 6 5 Selecting the check box will replace the entered answer value s with the check box value Entering the dimensions of a matrix will display any boxes necessary to crea matrix X Key Keyboard Sha Not Possible Submit Answe