Textbook Question
Perform each operation, if possible.
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7. Systems of Equations & Matrices
Determinants and Cramer's Rule
Multiple Choice
Evaluate the determinant of the matrix.
A
B
C
33
D
12
Verified step by step guidance1
Identify the elements of the 2x2 matrix: a = 4, b = \(\frac{9}{2}\), c = \(\frac{2}{3}\), d = 9.
Recall the formula for the determinant of a 2x2 matrix: det(A) = ad - bc.
Substitute the identified elements into the determinant formula: det(A) = (4)(9) - (\(\frac{9}{2}\))(\(\frac{2}{3}\)).
Calculate the product of the diagonal elements: 4 * 9.
Calculate the product of the off-diagonal elements: \(\frac{9}{2}\) * \(\frac{2}{3}\).
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