**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) No inverse

C)

D)

13)

A =

A)

B)

C) No inverse

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 + 4y = 20

3x + 5y = 4

A)

=

B)

=

C)

=

D)

=

20) 9x – 2y = 51

6y = 36

A)

=

B)

=

C)

=

D)

=

21) 5x + 2y – 2z = 37

4x + 3y + 5z = 22

7x – 2y + 6z = 15

A)

=

B)

=

C)

=

D)

=

22) 2x + 3z = 17

2y + 7z = 21

2x + 5y + 5z = 54

A)

=

B)

=

C)

=

D)

=

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

23)

=

A) 3x + 7y = 11

4x + 13y = 19

B) 7x + 3y = 11

13x + 4y = 19

C) 7x + 3y = -11

4x + 13y = -19

D) 7x + 3y = 11

4x + 13y = 19

24)

=

A) 2x + 8y = 6

3x – 6y = 9

B) 8x + 2y = 6

3x – 6y = 9

C) 8x + 2y = 6

-6x + 3y = 9

D) 8x + 2y = -6

3x – 6y = -9

25)

=

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

9x + 8y = 4

4x + 9z = 2

B) 2x – 5y + 7z = -2

9x + 8z = -4

4x + 9y = -2

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

9x + 8z = 4

4x + 9z = 2

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

9x + 8z = 4

4x + 9y = 2

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

26) x + 2y + 3z = -3

x + y + z = 12

2x + 2y+ z = 6

The inverse of is

A) {(51, 69, 30)}

B) {(-12, -24, 6)}

C) {(45, -51, 18)}

D) {(15, -60, 15)}

27) x + 2y + 3z = 7

x + y + z = 6

x – 2z = -6

The inverse of is

A) {(16, -21, 11)}

B) {(7, 0, 0)}

C) {(10, -14, 11)}

D) {(32, 39, 13)}

28) x + 2y + 3z = 2

x + y + z = 1

-x + y + 2z = -1

The inverse ofis

A) {(-3, 6, 1)}

B) {(2, 4, 2)}

C) {(2, -3, 2)}

D) {(2, 9, 6)}

**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 A^{-1} = to decode the cryptogram .

A) ACTS

B) ARMS

C) ALAS

D) ABLE

33) Use the coding matrix A = and its inverse A^{-1} = to decode the cryptogram .

A) DARE

B) CARE

C) BEAD

D) CURB

34) Use the coding matrix A = and its inverse A^{-1} = to decode the cryptogram .

A) GOOD_LUCK

B) STAY_CALM

C) HELP_THEM

D) LOOK_DOWN

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