Compute the determinants in Exercises 9–14 by cofactor expansions. At each step, choose a row or column that involves the least amount of computation

# Compute the determinants in Exercises 9–14 by cofactor expansions. At each step, choose a row or column that involves the least amount of computation

H
240 points

Compute the determinants in Exercises 9–14 by cofactor expansions. At each step, choose a row or column that involves the least amount of computation.

\begin{vmatrix} 6 & 3 & 2 & 4 & 0 \\ 9 & 0 & -4 & 1 & 0 \\ 8 & -5 & 6 & 7 & 1 \\ 2 & 0 & 0 & 0 & 0 \\ 4 & 2 & 3 & 2 & 0 \\ \end{vmatrix}

Compute the
hansel

8.7k points

first expand along the fifth column

$$(-1)^{3+5}(1) \begin{vmatrix} 6 & 3 & 2 & 4 \\ 9 & 0 & -4 & 1 \\ 2 & 0 & 0 & 0 \\ 4 & 2 & 3 & 2 \end{vmatrix}$$

then along the third row

$$(1)(-1)^{3+1}(3) \begin{vmatrix} 3 & 2 & 4 \\ 0 & -4 & 1 \\ 2 & 3 & 2 \end{vmatrix}$$

finally along the first column

$$(3)\bigg((-1)^{1+1}(3) \begin{vmatrix} -4 & 1 \\ 3 & 2 \\ \end{vmatrix} +(-1)^{3+1}(2) \begin{vmatrix} 2 & 4 \\ -4 & 1 \\ \end{vmatrix} \bigg) = (3)(3(-11)+2(18))=9$$

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