Question 5 • Advanced Algebra: Concepts and Connections
Based on the given information, what are the values of x and y of the solution to the system of equations used to create the information? absolute value of cap A is equal to the 2 by 2 matrix, row 1, column 1, 1 half column 2, 1 fourth row 2, column 1, 9 column 2, negative 3 , start absolute value cap A sub x end absolute value is equal to the 2 by 2 matrix, row 1, column 1, 5 column 2, 1 fourth row 2, column 1, 0 column 2, negative 3 , start absolute value cap A sub y end absolute value is equal to the 2 by 2 matrix, row 1, column 1, 1 half column 2, 5 row 2, column 1, 9 column 2, 0
Answer
A
x is equal to 1 over 12 comma y is equal to negative 1 fourth
B
x is equal to 4 comma y is equal to 12
C
x is equal to 12 comma y is equal to 4
D
x is equal to negative 1 fourth comma y is equal to 1 over 12
Explanation
Use Cramer's rule: x = det(Aₓ) / det(A) and y = det(Aᵧ) / det(A). The determinants are det(A) = (1/2)(−3) − (1/4)(9) = −15/4, det(Aₓ) = 5(−3) − (1/4)(0) = −15, and det(Aᵧ) = (1/2)(0) − 5(9) = −45. Thus x = 4 and y = 12, which is choice A.
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