Chapter 4: Q 246 (page 458)

Evaluate each determinant by expanding by minors.
$|\begin{matrix} 3 & 5 & 4 \\ - 1 & 3 & 0 \\ - 2 & 6 & 1 \end{matrix}|$

Short Answer

Expert verified

The required value of the determinant is $14$

Step by step solution

Step 1. Given information

The determinant is $|\begin{matrix} 3 & 5 & 4 \\ - 1 & 3 & 0 \\ - 2 & 6 & 1 \end{matrix}|$

Step 2. Expand by minors along the second row to evaluate determinant

$|\begin{matrix} 3 & 5 & 4 \\ - 1 & 3 & 0 \\ - 2 & 6 & 1 \end{matrix}| = - (- 1) |\begin{matrix} 5 & 4 \\ 6 & 1 \end{matrix}| + 3 |\begin{matrix} 3 & 4 \\ - 2 & 1 \end{matrix}| - 0 |\begin{matrix} 3 & 5 \\ - 2 & 6 \end{matrix}| = 1 [(5) (1) - (4) (6)] + 3 [(3) (1) - (4) (- 2)] - 0 = 1 [- 19] + 3 [11] - 0 = - 19 + 33 - 0 = 14$

Step 3. Required answer

The required value of the determinant is $14$

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Evaluate each determinant by expanding by minors.
$|\begin{matrix} 3 & 5 & 4 \\ - 1 & 3 & 0 \\ - 2 & 6 & 1 \end{matrix}|$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Expand by minors along the second row to evaluate determinant

Step 3. Required answer

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Evaluate each determinant by expanding by minors.354-130-261

Short Answer

Step by step solution

Step 1. Given information

Step 2. Expand by minors along the second row to evaluate determinant

Step 3. Required answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Probability and Statistics

Applied Mathematics

Geometry

Discrete Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Evaluate each determinant by expanding by minors.
$|\begin{matrix} 3 & 5 & 4 \\ - 1 & 3 & 0 \\ - 2 & 6 & 1 \end{matrix}|$