Q. 50 In Problems 43鈥�50, use propert... [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. 50 (page 741)

In Problems 43鈥�50, use properties of determinants to find the value of each determinant if it is known that
$|\begin{array}{llr} x & y & z \\ u & v & w \\ 1 & 2 & 3 \end{array}| = 4 |\begin{matrix} x + 3 & y + 6 & z + 9 \\ 3 u - 1 & 3 v - 2 & 3 w - 3 \\ 1 & 2 & 3 \end{matrix}|$

Short Answer

Expert verified

The value of the determinant is $12$ .

Step by step solution

Step 1. Given Information

We are given,

$|\begin{array}{llr} x & y & z \\ u & v & w \\ 1 & 2 & 3 \end{array}| = 4 |\begin{matrix} x + 3 & y + 6 & z + 9 \\ 3 u - 1 & 3 v - 2 & 3 w - 3 \\ 1 & 2 & 3 \end{matrix}|$

We have to solve the given determinant using properties of determinants.

Step 2. Solving the determinant

Using subtraction of determinant, we get

$|\begin{matrix} x + 3 & y + 6 & z + 9 \\ 3 u - 1 & 3 v - 2 & 3 w - 3 \\ 1 & 2 & 3 \end{matrix}| 鉄� |\begin{matrix} x + 3 & y + 6 & z + 9 \\ 3 u & 3 v & 3 w \\ 1 & 2 & 3 \end{matrix}| - |\begin{matrix} x + 3 & y + 6 & z + 9 \\ 1 & 2 & 3 \\ 1 & 2 & 3 \end{matrix}|$

Since the two rows of second determinant is same, so

role="math" $|\begin{matrix} x + 3 & y + 6 & z + 9 \\ 3 u - 1 & 3 v - 2 & 3 w - 3 \\ 1 & 2 & 3 \end{matrix}| 鉄� |\begin{matrix} x + 3 & y + 6 & z + 9 \\ 3 u & 3 v & 3 w \\ 1 & 2 & 3 \end{matrix}| - 0$

Using the addition of determinant, we get

$= |\begin{matrix} x & y & z \\ 3 u & 3 v & 3 w \\ 1 & 2 & 3 \end{matrix}| + |\begin{matrix} 3 & 6 & 9 \\ 3 u & 3 v & 3 w \\ 1 & 2 & 3 \end{matrix}|$

Step 3. Solving the determinant

Factoring out the GCF $3$ from the determinant, we get

role="math" localid="1647424003126" $= 3 |\begin{matrix} x & y & z \\ u & v & w \\ 1 & 2 & 3 \end{matrix}| + 3 |\begin{matrix} 1 & 2 & 3 \\ 3 u & 3 v & 3 w \\ 1 & 2 & 3 \end{matrix}| = 3 |\begin{matrix} x & y & z \\ u & v & w \\ 1 & 2 & 3 \end{matrix}| + 3 脳 0 = 3 脳 4 = 12$

Hence, the value of the determinant is $12$ .

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91影视

In Problems 43鈥�50, use properties of determinants to find the value of each determinant if it is known that
$|\begin{array}{llr} x & y & z \\ u & v & w \\ 1 & 2 & 3 \end{array}| = 4 |\begin{matrix} x + 3 & y + 6 & z + 9 \\ 3 u - 1 & 3 v - 2 & 3 w - 3 \\ 1 & 2 & 3 \end{matrix}|$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solving the determinant

Step 3. Solving the determinant

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91影视

In Problems 43鈥�50, use properties of determinants to find the value of each determinant if it is known thatxyzuvw123=4x+3y+6z+93u-13v-23w-3123

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solving the determinant

Step 3. Solving the determinant

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Statistics

Discrete Mathematics

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Geometry

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In Problems 43鈥�50, use properties of determinants to find the value of each determinant if it is known that
$|\begin{array}{llr} x & y & z \\ u & v & w \\ 1 & 2 & 3 \end{array}| = 4 |\begin{matrix} x + 3 & y + 6 & z + 9 \\ 3 u - 1 & 3 v - 2 & 3 w - 3 \\ 1 & 2 & 3 \end{matrix}|$