Q. 14 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. 14 (page 740)

Find the value of the determinant.
$|\begin{array}{ccc} 3 & 鈭� 9 & 4 \\ 1 & 4 & 0 \\ 8 & 鈭� 3 & 1 \end{array}|$

Short Answer

Expert verified

$|\begin{array}{ccc} 3 & 鈭� 9 & 4 \\ 1 & 4 & 0 \\ 8 & 鈭� 3 & 1 \end{array}| = - 119$

Step by step solution

Step 1. Given information

We have been given:

$|\begin{array}{ccc} 3 & 鈭� 9 & 4 \\ 1 & 4 & 0 \\ 8 & 鈭� 3 & 1 \end{array}|$

We have to find the value of this determinant.

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

$|\begin{array}{ccc} 3 & 鈭� 9 & 4 \\ 1 & 4 & 0 \\ 8 & 鈭� 3 & 1 \end{array}| = 3 鈰� |\begin{array}{cc} 4 & 0 \\ 鈭� 3 & 1 \end{array}| 鈭� (鈭� 9) 鈰� |\begin{array}{cc} 1 & 0 \\ 8 & 1 \end{array}| + 4 鈰� |\begin{array}{cc} 1 & 4 \\ 8 & 鈭� 3 \end{array}|$

Step 3. Simplify

$3 鈰� |\begin{array}{cc} 4 & 0 \\ 鈭� 3 & 1 \end{array}| 鈭� (鈭� 9) 鈰� |\begin{array}{cc} 1 & 0 \\ 8 & 1 \end{array}| + 4 鈰� |\begin{array}{cc} 1 & 4 \\ 8 & 鈭� 3 \end{array}|$

$= 3 鈰� [4 鈰� 1 鈭� (鈭� 3) 鈰� 0] + 9 鈰� [1 鈰� 1 鈭� 8 鈰� 0] + 4 鈰� [1 鈰� (鈭� 3) 鈭� 8 鈰� 4] = 3 鈰� (4 鈭� 0) + 9 鈰� (1 鈭� 0) + 4 鈰� (鈭� 3 鈭� 32) = 12 + 9 + 4 鈰� (鈭� 35) = = 21 鈭� 140 = - 119$

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91影视

Find the value of the determinant.
$|\begin{array}{ccc} 3 & 鈭� 9 & 4 \\ 1 & 4 & 0 \\ 8 & 鈭� 3 & 1 \end{array}|$

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.3鈭�941408鈭�31

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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Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Study anywhere. Anytime. Across all devices.

Find the value of the determinant.
$|\begin{array}{ccc} 3 & 鈭� 9 & 4 \\ 1 & 4 & 0 \\ 8 & 鈭� 3 & 1 \end{array}|$