Chapter 4: Q6. (page 194)

Find the value of each determinant.
6.
$|\begin{matrix} 1 & 3 & - 2 \\ 7 & 0 & 4 \\ - 3 & 5 & - 1 \end{matrix}|$

Short Answer

Expert verified

The value of the given determinant is $- 105$ .

Step by step solution

- Description of step.

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

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

- Find the value of the determinant.

The value of the determinant $|\begin{matrix} 1 & 3 & - 2 \\ 7 & 0 & 4 \\ - 3 & 5 & - 1 \end{matrix}|$ is given by:

$\begin{matrix} |\begin{matrix} 1 & 3 & - 2 \\ 7 & 0 & 4 \\ - 3 & 5 & - 1 \end{matrix}| = 1 |\begin{matrix} 0 & 4 \\ 5 & - 1 \end{matrix}| - 3 |\begin{matrix} 7 & 4 \\ - 3 & - 1 \end{matrix}| + (- 2) |\begin{matrix} 7 & 0 \\ - 3 & 5 \end{matrix}| \\ = 1 (0 - (20)) - 3 (- 7 - (- 12)) - 2 (35 + 0) \\ = 1 (- 20) - 3 (- 7 + 12) - 2 (35) \\ = - 20 - 3 (5) - 70 \\ = - 20 - 15 - 70 \\ = - 105 \end{matrix}$

- Description of step.

The value of the given determinant is $- 105$ .

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Find the value of each determinant.
6.
$|\begin{matrix} 1 & 3 & - 2 \\ 7 & 0 & 4 \\ - 3 & 5 & - 1 \end{matrix}|$

Short Answer

Step by step solution

- Description of step.

- Find the value of the determinant.

- Description of step.

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Find the value of each determinant.6.13-2704-35-1

Short Answer

Step by step solution

­- Description of step.

­- Find the value of the determinant.

­- Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Logic and Functions

Probability and Statistics

Mechanics Maths

Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

Find the value of each determinant.
6.
$|\begin{matrix} 1 & 3 & - 2 \\ 7 & 0 & 4 \\ - 3 & 5 & - 1 \end{matrix}|$

- Description of step.

- Find the value of the determinant.

- Description of step.