Chapter 4: Q. 7 (page 194)

Find the value of each determinant.
$|\begin{matrix} 3 & 4 & 4 \\ 2 & 1 & 5 \\ 0 & - 8 & 6 \end{matrix}|$

Short Answer

Expert verified

The value of the given determinant is 26.

Step by step solution

Step 1. Description of step.

The value of a third-order determinant by expansion along the first row can be found out by the following method:

$|\begin{matrix} a & b & c \\ d & e & f \\ g & h & i \end{matrix}| = a |\begin{matrix} e & f \\ h & i \end{matrix}| - b |\begin{matrix} d & f \\ g & i \end{matrix}| + c |\begin{matrix} d & e \\ g & h \end{matrix}|$

Step 2. Find the value of the determinant.

The value of the determinant $|\begin{matrix} 3 & 4 & 4 \\ 2 & 1 & 5 \\ 0 & - 8 & 6 \end{matrix}|$ is given by:

$\begin{matrix} |\begin{matrix} 3 & 4 & 4 \\ 2 & 1 & 5 \\ 0 & - 8 & 6 \end{matrix}| = 3 |\begin{matrix} 1 & 5 \\ - 8 & 6 \end{matrix}| - 4 |\begin{matrix} 2 & 5 \\ 0 & 6 \end{matrix}| + 4 |\begin{matrix} 2 & 1 \\ 0 & - 8 \end{matrix}| \\ = 3 (6 - (- 40)) - 4 (12 - 0) + 4 (- 16 - 0) \\ = 3 (6 + 40) - 4 (12) + 4 (- 16) \\ = 3 (46) - 4 (12) + 4 (- 16) \\ = 138 - 48 - 64 \\ = 26 \end{matrix}$

Step 3. Description of step.

The value of the given determinant is 26.

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Find the value of each determinant.
$|\begin{matrix} 3 & 4 & 4 \\ 2 & 1 & 5 \\ 0 & - 8 & 6 \end{matrix}|$

Short Answer

Step by step solution

Step 1. Description of step.

Step 2. Find the value of the determinant.

Step 3. Description of step.

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Find the value of each determinant.3442150-86

Short Answer

Step by step solution

Step 1. Description of step.

Step 2. Find the value of the determinant.

Step 3. Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Decision Maths

Calculus

Theoretical and Mathematical Physics

Pure Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Find the value of each determinant.
$|\begin{matrix} 3 & 4 & 4 \\ 2 & 1 & 5 \\ 0 & - 8 & 6 \end{matrix}|$