29
QuizMultiple Choice

Solving Matrix Equations — Quiz

Question 29 • Advanced Algebra: Concepts and Connections

Which equation can be used to solve the 2 by 2 matrix row 1, 2 6 row 2, 0 1 the 2 by 1 column matrix row 1 x sub 1 row 2 x sub 2 is equal to the 2 by 1 column matrix row 1 2 row 2 negative 3 ?

Answer
A
the 2 by 1 column matrix row 1 x sub 1 row 2 x sub 2 is equal to the 2 by 2 matrix row 1, 2 6 row 2, 0 1 the 2 by 1 column matrix row 1 2 row 2 negative 3
B
the 2 by 1 column matrix row 1 x sub 1 row 2 x sub 2 is equal to the 2 by 2 matrix, row 1, column 1, 0 point 5 column 2, negative 3 row 2, column 1, 0 column 2, 1 the 2 by 1 column matrix row 1 2 row 2 negative 3
C
the 2 by 1 column matrix row 1 x sub 1 row 2 x sub 2 is equal to the 2 by 2 matrix, row 1, column 1, 1 column 2, negative 6 row 2, column 1, 0 column 2, 2 the 2 by 1 column matrix row 1 2 row 2 negative 3
D
the 2 by 1 column matrix row 1 x sub 1 row 2 x sub 2 is equal to the 2 by 1 column matrix row 1 2 row 2 negative 3 the 2 by 2 matrix row 1, 2 6 row 2, 0 1

Explanation

To solve Mx = b for x, multiply both sides by the inverse of M = [[2, 6], [0, 1]]. Its inverse is [[0.5, -3], [0, 1]], since their product is the identity matrix. Therefore x = [[0.5, -3], [0, 1]][[2], [-3]], which is choice C.

AI-written and checked against the verified answer.

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