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Find the products AB and BA to determine whether B is the multiplicative

Question : Find the products AB and BA to determine whether B is the multiplicative : 2151858

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the products AB and BA to determine whether B is the multiplicative inverse of A.

1)

A = , B =

A) B = A-1

B) B ≠ A-1

2)

A = , B =

A) B ≠ A-1

B) B = A-1

3)

A = , B =

A) B ≠ A-1

B) B = A-1

4)

A = , B =

A) B ≠ A-1

B) B = A-1

5)

A = , B =

A) B = A-1

B) B ≠ A-1

6)

A = , B =

A) B = A-1

B) B ≠ A-1

7)

A = , B =

A) B ≠ A-1

B) B = A-1

8)

A = , B =

A) B = A-1

B) B ≠ A-1

9)

A = , B =

A) B ≠ A-1

B) B = A-1

Find the inverse of the matrix, if possible.

10)

A =

A)

B)

C)

D)

11)

A =

A)

B)

C)

D)

12)

A =

A)

B)

C)

D) No inverse

13)

A =

A)

B) No inverse

C)

D)

14)

A =

A)

B)

C)

D)

15)

A =

A)

B)

C)

D)

16)

A =

A)

B)

C)

D)

17)

A =

A)

B)

C)

D)

18)

A =

A)

B)

C)

D)

Write the linear system as a matrix equation in the form AX = B, where A is the coefficient matrix and B is the constant matrix.

19) 8x + 8y = 16

7x + 9y = 20

A)

  =

B)

  =

C)

  =

D)

  =

20) 5x - 2y = 18

8y = 48

A)

  =

B)

  =

C)

  =

D)

  =

21) 9x + 8y + 8z = -14

5x + 9y + 9z = -26

9x + 2y + 6z = 2

A)

  =

B)

  =

C)

  =

D)

  =

22) 8x + 8z = 56

2y + 8z = 52

4x + 9y + 7z = 97

A)

  =

B)

  =

C)

  =

D)

  =

Write the matrix equation as a system of linear equations without matrices.

23)

  =

A) 8x + 20y = 18

2x + 20y = 5

B) 20x + 8y = 18

2x + 20y = 5

C) 20x + 8y = -18

2x + 20y = - 5

D) 20x + 8y = 18

20x + 2y = 5

24)

  =

A) 8x + 2y = 3

-7x - 8y = -8

B) 8x + 2y = -3

-8x - 7y = 8

C) 8x + 2y = 3

-8x - 7y = -8

D) 2x + 8y = 3

-8x - 7y = -8

25)

  =

A) 5x - 7y + 4z = -2

4x + 8z = -4

6x + 9y = -2

B) 5x + 7y + 4z = -2

4x + 8y = 4

6x + 9z = 2

C) 5x + 7y + 4z = -2

4x + 8z = 4

6x + 9z = 2

D) 5x + 7y + 4z = -2

4x + 8z = 4

6x + 9y = 2

Solve the system using the inverse that is given for the coefficient matrix.

26) x + 2y + 3z = 2

x + y + z = -8

2x + 2y + z = 3

A) {(8, 16, 3)}

B) {(-10, 54, -17)}

C) {(-27, -32, -13)}

D) {(-37, 48, -19)}

27) x + 2y + 3z = 12

x + y + z = 1

x - 2z = -2

A) {(-19, 39, -8)}

B) {(12, 0, 0)}

C) {(-18, 27, -8)}

D) {(26, 37, 12)}

28) x + 2y + 3z = -4

x + y + z = 3

-x + y + 2z =-1

A) {(-15, 22, 11)}

B) {(-2, 1, 0)}

C) {(-4, 12, 2)}

D) {(-6, 25, -16)}

Encode or decode the given message, as requested, numbering the letters of the alphabet 1 through 26 in their usual order.

29) Use the coding matrix A =  to encode the message LIFE.

A)

B)

C)

D)

30) Use the coding matrix A =  to encode the message CARE.

A)

B)

C)

D)

31) Use the coding matrix A =  to encode the message COME_HERE.

A)

B)

C)

D)

32) Use the coding matrix A =  and its inverse  =  to decode the cryptogram  .

A) ABLE

B) ARMS

C) ALAS

D) ACTS

33) Use the coding matrix A =  and its inverse  =  to decode the cryptogram  .

A) BEAD

B) CURB

C) CARE

D) DARE

34) Use the coding matrix A =  and its inverse  =  to decode the cryptogram  .

A) STAY_CALM

B) GOOD_LUCK

C) LOOK_DOWN

D) HELP_THEM

Solution
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