Chapter 11: Q. 12 (page 740)

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

Short Answer

Expert verified

$|\begin{matrix} 1 & 3 & - 2 \\ 6 & 1 & - 5 \\ 8 & 2 & 3 \end{matrix}| = - 169$

Step by step solution

Step 1. Given information

We have been given:

$|\begin{matrix} 1 & 3 & - 2 \\ 6 & 1 & - 5 \\ 8 & 2 & 3 \end{matrix}|$

We have to find the value of this determinant.

Step 2. Use formula a11a12a13a21a22a23a31a32a33=a11a22a23a32a33-a12a21a23a31a33+a13a21a22a31a32.

$|\begin{array}{ccc} 1 & 3 & - 2 \\ 6 & 1 & - 5 \\ 8 & 2 & 3 \end{array}| = 1 \cdot |\begin{array}{cc} 1 & - 5 \\ 2 & 3 \end{array}| - 3 \cdot |\begin{array}{cc} 6 & - 5 \\ 8 & 3 \end{array}| + (- 2) \cdot |\begin{array}{cc} 6 & 1 \\ 8 & 2 \end{array}|$

Step 3. Simplify

$1 \cdot |\begin{array}{cc} 1 & - 5 \\ 2 & 3 \end{array}| - 3 \cdot |\begin{array}{cc} 6 & - 5 \\ 8 & 3 \end{array}| + (- 2) \cdot |\begin{array}{cc} 6 & 1 \\ 8 & 2 \end{array}| = 1 \cdot [1 \cdot 3 - 2 \cdot (- 5)] - 3 \cdot [6 \cdot 3 - 8 \cdot (- 5)] - 2 \cdot [6 \cdot 2 - 8 \cdot 1] = 1 \cdot (3 + 10) - 3 \cdot (18 + 40) - 2 \cdot (12 - 8) = 1 \cdot 13 - 3 \cdot 58 - 2 \cdot 4 = 13 - 174 - 8 = - 169$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

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

Short Answer

Step by step solution

Step 1. Given information

Step 2. Use formula a11a12a13a21a22a23a31a32a33=a11a22a23a32a33-a12a21a23a31a33+a13a21a22a31a32.

Step 3. Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

Pure Maths

Calculus

Decision Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Find the value of the determinant.13-261-5823

Short Answer

Step by step solution

Step 1. Given information

Step 2. Use formula a11a12a13a21a22a23a31a32a33=a11a22a23a32a33-a12a21a23a31a33+a13a21a22a31a32.

Step 3. Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

Pure Maths

Calculus

Decision Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

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