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

Step 1 Given determinant is,

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

Evaluate the determinant.

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

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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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

Step by step solution

Step 1 Given determinant is,

Step 2 Now simplify it.

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In Problems 7-14, find the value of each determinant.ABC214131

Short Answer

Step by step solution

Step 1 Given determinant is,

Step 2 Now simplify it.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Theoretical and Mathematical Physics

Pure Maths

Decision Maths

Probability and Statistics

Calculus

Study anywhere. Anytime. Across all devices.

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