Chapter 4: Q 4.93 (page 453)

Evaluate the determinant $[\begin{matrix} 3 & - 2 & 4 \\ 0 & - 1 & - 2 \\ 2 & 3 & - 1 \end{matrix}]$ , by expanding by minors along the first row.

Short Answer

Expert verified

The value of the determinant is 37.

Step by step solution

Step 1. Given information

The given determinant is

$[\begin{matrix} 3 & - 2 & 4 \\ 0 & - 1 & - 2 \\ 2 & 3 & - 1 \end{matrix}]$

Step 2. Calculation

Expand by minors along the first row

$3 [\begin{matrix} - 1 & - 2 \\ 3 & - 1 \end{matrix}] - (- 2) [\begin{matrix} 0 & - 2 \\ 2 & - 1 \end{matrix}] + 4 [\begin{matrix} 0 & - 1 \\ 2 & 3 \end{matrix}] = 3 (1 - (- 2 \times 3)) + 2 ((0 \times - 1) - (- 2 \times 2)) + 4 (3 \times 0 - (- 1 \times 2)) = 3 (1 + 6) + 2 (0 + 4) + 4 (0 + 2) = 3 \times 7 + 2 \times 4 + 4 \times 2 = 21 + 8 + 8 = 37$

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Evaluate the determinant $[\begin{matrix} 3 & - 2 & 4 \\ 0 & - 1 & - 2 \\ 2 & 3 & - 1 \end{matrix}]$ , by expanding by minors along the first row.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

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Short Answer

Step by step solution

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Evaluate the determinant $[\begin{matrix} 3 & - 2 & 4 \\ 0 & - 1 & - 2 \\ 2 & 3 & - 1 \end{matrix}]$ , by expanding by minors along the first row.