Q. 12 Find the value of the determinan... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

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.

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

Step 3. Simplify

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

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91影视

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

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91影视

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

Logic and Functions

Discrete Mathematics

Statistics

Theoretical and Mathematical Physics

Pure Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

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