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Question 6.1.8: Find det A for A=[0 2 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 2 3 0 0 ......

Find det A for

A=\begin{bmatrix}0&2&0&0&0&0\\0&0&0&8&0&0\\0&0&0&0&0&2\\3&0&0&0&0&0\\0&0&0&0&5&0\\0&0&1&0&0&0\end{bmatrix}.

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Only one pattern P makes a nonzero contribution toward the determinant:

Thus, \rm{det \ A = (sgn \ P)(prod \ P) }= (−1)^72 · 8 · 2 · 3 · 5 · 1 = −480.

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