21
QuizMultiple Choice

Solving Matrix Equations — Quiz

Question 21 • Advanced Algebra: Concepts and Connections

The matrix equation can be used to solve a system of linear equations. What is the solution to the system? the 2 by 2 matrix row 1, 6 4 row 2, 9 6 the 2 by 1 column matrix x y is equal to the 2 by 1 column matrix 1 3

Answer
A
x is equal to 1 half , y is equal to 1
B
x is equal to 1 tenth , y is equal to 1 fifth
C
The system has infinite solutions.
D
The system has no solution.

Explanation

The matrix equation represents 6x + 4y = 1 and 9x + 6y = 3. The left side of the second equation is 1.5 times the left side of the first, so the right side would also need to be 1.5 times 1, or 1.5. Instead, it is 3, so the equations contradict each other. Therefore, the system has no solution (choice D).

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