17
QuizMultiple Choice

Matrices and Row Operations — Quiz

Question 17 • Advanced Algebra: Concepts and Connections

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?

Answer
A
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
B
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
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, 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

Explanation

Write the coefficients of x, y, and z in order, then place each equation’s constant on the right side of the divider. The equations give the rows [1, 2, 0, 3], [-1, 1, 1, 2], and [0, 1, -2, -3]. Choice B has exactly these rows in its 3-by-4 augmented matrix.

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