Question 15.RW.11: Derive the determinant of matrix A = [ 4 6 1 2 5 2 9 0 4 ] b......

Basic Mathematics for Economists [1185418]

Derive the determinant of matrix A = $\begin{bmatrix}4& 6 &1 \\ 2& 5& 2 \\ 9 &0 &4 \end{bmatrix}$ by expanding along the 3rd row.

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Expanding across the 3rd row, the first term will have a positive sign and so

|A| = 9 $\begin{vmatrix} 6 & 1 \\ 5& 2 \end{vmatrix}$ − 0 $\begin{vmatrix} 4 & 1 \\ 2& 2 \end{vmatrix}$ + 4 $\begin{vmatrix} 4 & 6 \\ 2& 5 \end{vmatrix}$
= 9(12 − 5) − 0 + 4(20 − 12) = 63 + 32 = 95

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