Matrices and Sequences — Test

Question 15 • Algebra II

Which is a coefficient matrix for the system of linear equations? 6 A plus 2 b is equal to 22 negative 8 b minus 3 c is equal to negative 19 negative 10 A plus 9 c is equal to negative 12

Answer

the 3 by 3 matrix, row 1, column 1, 6 column 2, 2 column 3, 0 row 2, column 1, 0 column 2, negative 8 column 3, negative 3 row 3, column 1, negative 10 column 2, 0 column 3, 9

the 3 by 3 matrix row 1, 6 2 0 row 2, 0 8 3 row 3, 10 0 9

the 3 by 4 matrix, row 1, column 1, 6 column 2, 2 column 3, 0 column 4, 22 row 2, column 1, 0 column 2, negative 8 column 3, negative 3 column 4, negative 19 row 3, column 1, negative 10 column 2, 0 column 3, 9 column 4, negative 12

the 3 by 3 matrix, row 1, column 1, 6 column 2, 2 column 3, 22 row 2, column 1, negative 8 column 2, negative 3 column 3, negative 19 row 3, column 1, negative 10 column 2, 9 column 3, negative 12

Explanation

A coefficient matrix lists only the coefficients of the variables, in the same variable order for every row. Using the order A, b, c, the equations give rows (6, 2, 0), (0, −8, −3), and (−10, 0, 9). The constants 22, −19, and −12 are not included, so the correct choice is the 3-by-3 matrix in A.

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