28
QuizMultiple Choice

Introduction to Matrices — Quiz

Question 28 • Advanced Algebra: Concepts and Connections

Dakarai wrote the system of linear equations. 7 x plus 8 y is equal to 28 negative 3 x plus 9 y is equal to negative 24 Dakarai then wrote the coefficient matrix that represents this system. Which matrix could she have written?

Answer
A
the 2 by 3 matrix, row 1, column 1, 7 column 2, negative 3 column 3, 28 row 2, column 1, 8 column 2, 9 column 3, negative 24
B
the 2 by 2 matrix, row 1, column 1, 7 column 2, 8 row 2, column 1, negative 3 column 2, 9
C
the 2 by 2 matrix, row 1, column 1, 7 column 2, negative 3 row 2, column 1, 8 column 2, 9
D
the 2 by 3 matrix, row 1, column 1, 7 column 2, 8 column 3, 28 row 2, column 1, negative 3 column 2, 9 column 3, negative 24

Explanation

A coefficient matrix contains only the coefficients of the variables, not the constants on the right side of the equations. In the first equation, the coefficients of x and y are 7 and 8; in the second, they are −3 and 9. Thus the matrix is [[7, 8], [−3, 9]], which is choice B.

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