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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. 12 (page 627)

In Problems $7 - 14$ , find the value of each determinant.
$|\begin{matrix} A & B & C \\ 0 & 2 & 4 \\ 3 & 1 & 3 \end{matrix}|$

Short Answer

Expert verified

The value of the determinant $|\begin{matrix} A & B & C \\ 0 & 2 & 4 \\ 3 & 1 & 3 \end{matrix}|$ is, $2 A + 12 B - 6 C$ .

Step by step solution

01

Step 1 Given determinant is,

$|\begin{matrix} A & B & C \\ 0 & 2 & 4 \\ 3 & 1 & 3 \end{matrix}|$

Evaluate the determinant.

$|\begin{matrix} A & B & C \\ 0 & 2 & 4 \\ 3 & 1 & 3 \end{matrix}| = A [2 (3) - 4 (1)] - B [0 (3) - 4 (3)] + C [0 (1) - 2 (3)]$

02

Step 2 Now simplify it.

$|\begin{matrix} A & B & C \\ 0 & 2 & 4 \\ 3 & 1 & 3 \end{matrix}| = A [6 - 4] - B [0 - 12] + C [0 - 6] = A [2] - B [- 12] + C [- 6] = 2 A + 12 B - 6 C$

Thus, the value of the determinant is, $2 A + 12 B - 6 C$ .

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