If Q is\( \left[ \begin{array}{cc} 9 & -2 \\ -7 & 4 \\ \end{array} \right]\) , then |Q| is?
The correct answer is C. 22
The determinant of a 2x2 matrix is given by the formula |Q| = ad - bc, where a, b, c, and d are the elements of the matrix Q arranged as follows:
Q = \( \left[ \begin{array}{cc} a & b \\ c & d \\ \end{array} \right]\)
In this case, the matrix Q is given as:
Q = \( \left[ \begin{array}{cc} 9 & -2 \\ -7 & 4 \\ \end{array} \right]\)
So, a = 9, b = -2, c = -7, and d = 4. Substituting these values into the formula for the determinant of a 2x2 matrix, we get:
|Q| = ad - bc
= (9)(4) - (-2)(-7)
= 36 - 14= 22
So, the determinant of the matrix Q is 22.
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