Chapter 4: Q 247 (page 458)

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

Short Answer

Expert verified

The required value of the determinant is $25$

Step by step solution

Step 1. Given information

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

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

$|\begin{matrix} 2 & - 4 & - 3 \\ 5 & - 1 & - 4 \\ 3 & 2 & 0 \end{matrix}| = 3 |\begin{matrix} - 4 & - 3 \\ - 1 & - 4 \end{matrix}| - 2 |\begin{matrix} 2 & - 3 \\ 5 & - 4 \end{matrix}| + 0 |\begin{matrix} 2 & - 4 \\ 5 & - 1 \end{matrix}| = 3 [(- 4) (- 4) - (- 3) (- 1)] - 2 [(2) (- 4) - (- 3) (5)] + 0 = 3 [13] - 2 [7] + 0 = 39 - 14 + 0 = 25$

Step 3. Required answer

The required value of the determinant is $25$

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

Short Answer

Step by step solution

Step 1. Given information

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

Step 3. Required answer

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Evaluate each determinant by expanding by minors.2-4-35-1-4320

Short Answer

Step by step solution

Step 1. Given information

Step 2. Expand by minors along the third 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

Mechanics Maths

Theoretical and Mathematical Physics

Decision Maths

Probability and Statistics

Geometry

Study anywhere. Anytime. Across all devices.

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