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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 9: Q. 13 (page 627)

In Problems $7 - 14$ , find the value of each determinant.
$|\begin{matrix} A & B & C \\ - 1 & 3 & 5 \\ 5 & 0 & - 2 \end{matrix}|$

Short Answer

Expert verified

The value of the determinant $|\begin{matrix} A & B & C \\ - 1 & 3 & 5 \\ 5 & 0 & - 2 \end{matrix}|$ is, $- 6 A + 23 B - 15 C$ .

Step by step solution

01

Step 1 Given determinant is,

$|\begin{matrix} A & B & C \\ - 1 & 3 & 5 \\ 5 & 0 & - 2 \end{matrix}|$

Evaluate the determinant.

role="math" localid="1646807619254" $|\begin{matrix} A & B & C \\ - 1 & 3 & 5 \\ 5 & 0 & - 2 \end{matrix}| = A [3 (- 2) - 5 (0)] - B [- 2 (- 1) - 5 (5)] + C [- 1 (0) - 3 (5)]$

02

Step 2 Now simplify it.

$|\begin{matrix} A & B & C \\ - 1 & 3 & 5 \\ 5 & 0 & - 2 \end{matrix}| = = A [- 6 - 0] - B [2 - 25] + C [- 15] = A [- 6] - B [- 23] + C [- 15] = - 6 A + 23 B - 15 C$

Thus, the value of the determinant is, $- 6 A + 23 B - 15 C$ .

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