Chapter 4: Q48. (page 187)

Find the value of det A if $A = [\begin{matrix} 0 & 3 & - 2 \\ - 4 & 0 & 1 \\ 3 & 2 & 0 \end{matrix}]$ .
$A . 0 B. 12 C. 25 D. 36$

Short Answer

Expert verified

The value of the determinant is $| A | = 25$ .

Step by step solution

Step 1- Apply the concept of determinant.

The determinant is a scalar value that is a function of the entries of a square matrix. It allows characterizing some properties of the matrix and the linear map represented by the matrix.

Step 2- Step description.

Consider the matrix $A = (\begin{matrix} 0 & 3 & - 2 \\ - 4 & 0 & 1 \\ 3 & 2 & 0 \end{matrix})$ .

find the value of the determinant as follows:

$\begin{matrix} | A | = 0 \cdot \det (\begin{matrix} 0 & 1 \\ 2 & 0 \end{matrix}) - 3 \cdot \det (\begin{matrix} - 4 & 1 \\ 3 & 0 \end{matrix}) - 2 \cdot \det (\begin{matrix} - 4 & 0 \\ 3 & 2 \end{matrix}) \\ = 0 \cdot (- 2) - 3 (- 3) - 2 (- 8) \\ = 25 \end{matrix}$

Step 3- Step description.

Therefore, the value of the determinant is 25.

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Find the value of det A if $A = [\begin{matrix} 0 & 3 & - 2 \\ - 4 & 0 & 1 \\ 3 & 2 & 0 \end{matrix}]$ .
$A . 0 B. 12 C. 25 D. 36$

Short Answer

Step by step solution

Step 1- Apply the concept of determinant.

Step 2- Step description.

Step 3- Step description.

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Find the value of det A if A=03−2−401320.A.0 B. 12 C. 25 D. 36

Short Answer

Step by step solution

Step 1- Apply the concept of determinant.

Step 2- Step description.

Step 3- Step description.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Theoretical and Mathematical Physics

Statistics

Applied Mathematics

Decision Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

Find the value of det A if $A = [\begin{matrix} 0 & 3 & - 2 \\ - 4 & 0 & 1 \\ 3 & 2 & 0 \end{matrix}]$ .
$A . 0 B. 12 C. 25 D. 36$