# Evaluate the determinant of each of the following matrices: a. begin{bmatrix}10 & 9 6 & 5 end{bmatrix} b. begin{bmatrix}4 & 3 -5 & -8 end{bmatrix}

Evaluate the determinant of each of the following matrices:
a. $\left[\begin{array}{cc}10& 9\\ 6& 5\end{array}\right]$
b. $\left[\begin{array}{cc}4& 3\\ -5& -8\end{array}\right]$
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Step 1
We have to evaluate the determinant of each of the following matrices:
a. $\left[\begin{array}{cc}10& 9\\ 6& 5\end{array}\right]$
b. $\left[\begin{array}{cc}4& 3\\ -5& -8\end{array}\right]$
We know the value of determinant of matrix will be calculated in the following ways: $\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]=|\begin{array}{cc}a& b\\ c& d\end{array}|$
$=a×d-b×c$
So calculating for part (a),
$\left[\begin{array}{cc}10& 9\\ 6& 5\end{array}\right]=|\begin{array}{cc}10& 9\\ 6& 5\end{array}|$
$=10×5-9×6$
$=50-54$
$=-4$
Hence, value of determinant is -4.
Step 2
calculating for part (b),
$\left[\begin{array}{cc}4& 3\\ -5& -8\end{array}\right]=|\begin{array}{cc}4& 3\\ -5& -8\end{array}|$
$=4×\left(-8\right)-3×\left(-5\right)$
$=-32+15$
$=-17$
Hence, value of determinant is -17.
Jeffrey Jordon