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Matrices and Row Operations — Quiz Answers

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1
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The drama club at a local high school sells adult, teen, and child tickets for a school play. The matrix represents the tickets sold and the total cost of the tickets for three performances. the 3 by 4 matrix, row 1, column 1, 3 column 2, 12 column 3, 6 column 4, 102 row 2, column 1, 6 column 2, 18 column 3, 6 column 4, 162 row 3, column 1, 0 column 2, 15 column 3, 5 column 4, 85 Which of the following is the result of performing the row operation negative 2 cap r 1 plus cap r 2 rightarrow cap r 2 on this matrix?

A
the 3 by 4 matrix, row 1, column 1, 3 column 2, 12 column 3, 6 column 4, 102 row 2, column 1, 0 column 2, negative 6 column 3, negative 6 column 4, negative 42 row 3, column 1, 0 column 2, 15 column 3, 5 column 4, 85
B
the 3 by 4 matrix, row 1, column 1, negative 6 column 2, negative 24 column 3, negative 12 column 4, negative 204 row 2, column 1, 6 column 2, 18 column 3, 6 column 4, 162 row 3, column 1, 0 column 2, 15 column 3, 5 column 4, 85
C
the 3 by 4 matrix, row 1, column 1, 3 column 2, 6 column 3, 6 column 4, 102 row 2, column 1, 6 column 2, 6 column 3, 6 column 4, 162 row 3, column 1, 0 column 2, 15 column 3, 5 column 4, 85
D
the 3 by 4 matrix, row 1, column 1, 0 column 2, negative 6 column 3, negative 6 column 4, negative 42 row 2, column 1, 6 column 2, 18 column 3, 6 column 4, 162 row 3, column 1, 0 column 2, 15 column 3, 5 column 4, 85
2
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The augmented matrix below represents a system of equations. the 3 by 4 matrix, row 1, column 1, negative 1 column 2, 1 column 3, 2 column 4, 7 row 2, column 1, negative 3 column 2, 2 column 3, 1 column 4, 4 row 3, column 1, 2 column 2, 1 column 3, 1 column 4, 7 Which matrix results from the operation cap r 1 left right arrow cap r 2 ?

A
the 3 by 4 matrix, row 1, column 1, negative 3 column 2, 2 column 3, 1 column 4, 4 row 2, column 1, negative 1 column 2, 1 column 3, 2 column 4, 7 row 3, column 1, 2 column 2, 1 column 3, 1 column 4, 7
B
the 3 by 4 matrix, row 1, column 1, negative 3 column 2, 2 column 3, 1 column 4, 7 row 2, column 1, negative 1 column 2, 1 column 3, 2 column 4, 4 row 3, column 1, 2 column 2, 1 column 3, 1 column 4, 7
C
the 3 by 4 matrix, row 1, column 1, 1 column 2, negative 1 column 3, 2 column 4, 7 row 2, column 1, 2 column 2, negative 3 column 3, 1 column 4, 4 row 3, column 1, 1 column 2, 2 column 3, 1 column 4, 7
D
the 3 by 4 matrix, row 1, column 1, negative 1 column 2, 1 column 3, 2 column 4, 7 row 2, column 1, negative 1 column 2, 1 column 3, 2 column 4, 7 row 3, column 1, 2 column 2, 1 column 3, 1 column 4, 7
3

Kamal wrote the augmented matrix to represent a system of equations. the 3 by 4 matrix, row 1, column 1, 1 column 2, 0 column 3, 1 column 4, negative 1 row 2, column 1, 1 column 2, 3 column 3, negative 1 column 4, negative 9 row 3, column 1, 3 column 2, 2 column 3, 0 column 4, negative 2 Which matrix results from the operation negative 3 cap r 2 left right arrow cap r 2 ?

A
the 3 by 4 matrix, row 1, column 1, 1 column 2, 0 column 3, 1 column 4, negative 1 row 2, column 1, negative 3 column 2, negative 9 column 3, 3 column 4, 27 row 3, column 1, 3 column 2, 2 column 3, 0 column 4, negative 2
B
the 3 by 4 matrix, row 1, column 1, 1 column 2, 0 column 3, 1 column 4, negative 1 row 2, column 1, negative 2 column 2, 0 column 3, negative 4 column 4, negative 12 row 3, column 1, 3 column 2, 2 column 3, 0 column 4, negative 2
C
the 3 by 4 matrix, row 1, column 1, 1 column 2, 0 column 3, 1 column 4, negative 1 row 2, column 1, negative 3 column 2, negative 9 column 3, 3 column 4, negative 9 row 3, column 1, 3 column 2, 2 column 3, 0 column 4, negative 2
D
the 3 by 4 matrix, row 1, column 1, 1 column 2, 0 column 3, 1 column 4, negative 1 row 2, column 1, negative 3 column 2, negative 3 column 3, negative 3 column 4, negative 3 row 3, column 1, 3 column 2, 2 column 3, 0 column 4, negative 2
4

Juanita wants to perform row operations on the augmented matrix for the system. x plus 2 y is equal to 3 negative x plus y plus z is equal to 2 y minus 2 z is equal to negative 3 Which matrix should Juanita use to perform the operations?

A
the 3 by 4 matrix, row 1, column 1, 1 column 2, 2 column 3, 3 column 4, 0 row 2, column 1, negative 1 column 2, 1 column 3, 1 column 4, 2 row 3, column 1, 1 column 2, negative 2 column 3, negative 3 column 4, 0
B
the 3 by 4 matrix, row 1, column 1, 1 column 2, 2 column 3, 0 column 4, 3 row 2, column 1, negative 1 column 2, 1 column 3, 1 column 4, 2 row 3, column 1, 0 column 2, 1 column 3, negative 2 column 4, negative 3
C
the 3 by 3 matrix, row 1, column 1, 1 column 2, 2 column 3, 0 row 2, column 1, negative 1 column 2, 1 column 3, 1 row 3, column 1, 0 column 2, 1 column 3, negative 2
D
the 3 by 4 matrix, row 1, column 1, 1 column 2, 0 column 3, 0 column 4, 3 row 2, column 1, 0 column 2, 1 column 3, 0 column 4, 2 row 3, column 1, 0 column 2, 0 column 3, 2 column 4, negative 3
5

A student performed row operations on a matrix as shown. Student's Work [−41240−1313245]→[−41240−13130107] Which operations did the student perform?

A
2 cap r 2 left right arrow cap r 3
B
2 cap r 2 plus cap r 3 rightarrow cap r 3
C
2 cap r 2 plus cap r 3 rightarrow cap r 2 comma cap r 3
D
2 cap r 3 plus negative cap r 3 rightarrow cap r 3
6

The matrix represents a system of equations. the 3 by 4 matrix, row 1, column 1, 2 column 2, negative 1 column 3, negative 3 column 4, negative 20 row 2, column 1, negative 2 column 2, negative 6 column 3, 6 column 4, negative 4 row 3, column 1, 0 column 2, 3 column 3, negative 2 column 4, negative 9 Which matrix represents 1 half cap r 2 plus cap r 3 rightarrow cap r 3 ?

A
the 3 by 4 matrix, row 1, column 1, 2 column 2, negative 1 column 3, negative 3 column 4, negative 20 row 2, column 1, negative 2 column 2, negative 6 column 3, 6 column 4, negative 4 row 3, column 1, negative 2 column 2, negative 3 column 3, 4 column 4, negative 13
B
the 3 by 4 matrix, row 1, column 1, 2 column 2, negative 1 column 3, negative 3 column 4, negative 20 row 2, column 1, negative 1 column 2, negative 3 column 3, 3 column 4, negative 2 row 3, column 1, 0 column 2, 3 column 3, negative 2 column 4, negative 9
C
the 3 by 4 matrix, row 1, column 1, 2 column 2, negative 1 column 3, negative 3 column 4, negative 20 row 2, column 1, negative 2 column 2, negative 6 column 3, 6 column 4, negative 4 row 3, column 1, negative 1 column 2, 0 column 3, 1 column 4, negative 11
D
the 3 by 4 matrix, row 1, column 1, 2 column 2, negative 1 column 3, negative 3 column 4, negative 20 row 2, column 1, negative 1 column 2, negative 3 column 3, 3 column 4, negative 2 row 3, column 1, 0 column 2, 6 column 3, negative 4 column 4, negative 18
9

The matrix represents a system of equations. the 3 by 4 matrix, row 1, column 1, 2 column 2, negative 1 column 3, negative 3 column 4, negative 20 row 2, column 1, negative 2 column 2, negative 6 column 3, 6 column 4, negative 4 row 3, column 1, 0 column 2, 3 column 3, negative 2 column 4, negative 9 Which matrix represents 1 half cap r 2 plus cap r 3 rightarrow cap r 3 ?

A
the 3 by 4 matrix, row 1, column 1, 2 column 2, negative 1 column 3, negative 3 column 4, negative 20 row 2, column 1, negative 1 column 2, negative 3 column 3, 3 column 4, negative 2 row 3, column 1, 0 column 2, 6 column 3, negative 4 column 4, negative 18
B
the 3 by 4 matrix, row 1, column 1, 2 column 2, negative 1 column 3, negative 3 column 4, negative 20 row 2, column 1, negative 2 column 2, negative 6 column 3, 6 column 4, negative 4 row 3, column 1, negative 1 column 2, 0 column 3, 1 column 4, negative 11
C
the 3 by 4 matrix, row 1, column 1, 2 column 2, negative 1 column 3, negative 3 column 4, negative 20 row 2, column 1, negative 2 column 2, negative 6 column 3, 6 column 4, negative 4 row 3, column 1, negative 2 column 2, negative 3 column 3, 4 column 4, negative 13
D
the 3 by 4 matrix, row 1, column 1, 2 column 2, negative 1 column 3, negative 3 column 4, negative 20 row 2, column 1, negative 1 column 2, negative 3 column 3, 3 column 4, negative 2 row 3, column 1, 0 column 2, 3 column 3, negative 2 column 4, negative 9
10

The drama club at a local high school sells adult, teen, and child tickets for a school play. The matrix represents the tickets sold and the total cost of the tickets for three performances. the 3 by 4 matrix, row 1, column 1, 3 column 2, 12 column 3, 6 column 4, 102 row 2, column 1, 6 column 2, 18 column 3, 6 column 4, 162 row 3, column 1, 0 column 2, 15 column 3, 5 column 4, 85 Which of the following is the result of performing the row operation negative 2 cap r 1 plus cap r 2 rightarrow cap r 2 on this matrix?

A
the 3 by 4 matrix, row 1, column 1, 3 column 2, 6 column 3, 6 column 4, 102 row 2, column 1, 6 column 2, 6 column 3, 6 column 4, 162 row 3, column 1, 0 column 2, 15 column 3, 5 column 4, 85
B
the 3 by 4 matrix, row 1, column 1, 0 column 2, negative 6 column 3, negative 6 column 4, negative 42 row 2, column 1, 6 column 2, 18 column 3, 6 column 4, 162 row 3, column 1, 0 column 2, 15 column 3, 5 column 4, 85
C
the 3 by 4 matrix, row 1, column 1, 3 column 2, 12 column 3, 6 column 4, 102 row 2, column 1, 0 column 2, negative 6 column 3, negative 6 column 4, negative 42 row 3, column 1, 0 column 2, 15 column 3, 5 column 4, 85
D
the 3 by 4 matrix, row 1, column 1, negative 6 column 2, negative 24 column 3, negative 12 column 4, negative 204 row 2, column 1, 6 column 2, 18 column 3, 6 column 4, 162 row 3, column 1, 0 column 2, 15 column 3, 5 column 4, 85

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