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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. 11 (page 627)

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

Short Answer

Expert verified

The value of the determinant $|\begin{matrix} A & B & C \\ 2 & 1 & 4 \\ 1 & 3 & 1 \end{matrix}|$ is, $- 11 A + 2 B + 5 C$ .

Step by step solution

01

Step 1 Given determinant is,

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

Evaluate the determinant.

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

02

Step 2 Now simplify it.

$|\begin{matrix} A & B & C \\ 2 & 1 & 4 \\ 1 & 3 & 1 \end{matrix}| = A [1 - 12] - B [2 - 4] + C [6 - 1] = A [- 11] - B [- 2] + C [5] = - 11 A + 2 B + 5 C$

Thus, the value of the determinant $|\begin{matrix} A & B & C \\ 2 & 1 & 4 \\ 1 & 3 & 1 \end{matrix}|$ is, $- 11 A + 2 B + 5 C$ .

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