Question 6.1.9: Find det A for A=[6 0 1 0 0 9 3 2 3 7 8 0 3 2 9 0 0 4 0 0 5 ......

Linear Algebra with Applications [1016048]

Find det A for

$A=\begin{bmatrix}6&0&1&0&0\\9&3&2&3&7\\8&0&3&2&9\\0&0&4&0&0\\5&0&5&0&1\end{bmatrix}$ .

Step-by-Step

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Again, let’s look for patterns with a nonzero product. We pick the entries column by column this time. In the second column, we must choose the second component, 3. Then, in the fourth column, we must choose the third component, 2. Next, think about the last column, and so on. It turns out that there is only one pattern P with a nonzero product.

$\rm{det \ A = (sgn \ P)(prod \ P)} = (−1)^1 6 · 3 · 2 · 4 · 1 = −144.$ .

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