Q. 45 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. 45 (page 741)

In Problems 43鈥�50, use properties of determinants to find the value of each determinant if it is known that $|\begin{matrix} x & y & z \\ u & v & w \\ 1 & 2 & 3 \end{matrix}| = 4$
role="math" localid="1647384474767" $|\begin{matrix} x & y & z \\ - 3 & - 6 & - 9 \\ u & v & w \end{matrix}|$

Short Answer

Expert verified

The value of the determinant $|\begin{matrix} x & y & z \\ - 3 & - 6 & - 9 \\ u & v & w \end{matrix}|$ is $12$

role="math" localid="1647384923415" $|\begin{matrix} x & y & z \\ - 3 & - 6 & - 9 \\ u & v & w \end{matrix}| = 12$

Step by step solution

Step 1. Given information

The given determinant is

$|\begin{matrix} x & y & z \\ - 3 & - 6 & - 9 \\ u & v & w \end{matrix}|$

Step 2. Value of determinant

Use the property of determinant and take $- 3$ common form second row of determinants

role="math" localid="1647384792440" $|\begin{matrix} x & y & z \\ - 3 & - 6 & - 9 \\ u & v & w \end{matrix}| = |\begin{matrix} x & y & z \\ - 3 (1) & - 3 (2) & - 3 (3) \\ u & v & w \end{matrix}| = - 3 |\begin{matrix} x & y & z \\ 1 & 2 & 3 \\ u & v & w \end{matrix}|$

Use the property of determinant and interchange the second and third-row

$|\begin{matrix} x & y & z \\ - 3 & - 6 & - 9 \\ u & v & w \end{matrix}| = - 3 |\begin{matrix} x & y & z \\ 1 & 2 & 3 \\ u & v & w \end{matrix}| = (- 3) (- 1) |\begin{matrix} x & y & z \\ u & v & w \\ 1 & 2 & 3 \end{matrix}| = (- 3) (- 1) (4) = 12$

So the value of the determinant is $|\begin{matrix} x & y & z \\ - 3 & - 6 & - 9 \\ u & v & w \end{matrix}| = 12$

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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 $|\begin{matrix} x & y & z \\ u & v & w \\ 1 & 2 & 3 \end{matrix}| = 4$
role="math" localid="1647384474767" $|\begin{matrix} x & y & z \\ - 3 & - 6 & - 9 \\ u & v & w \end{matrix}|$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Value of determinant

One App. One Place for Learning.

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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 xyzuvw123=4role="math" localid="1647384474767" xyz-3-6-9uvw

Short Answer

Step by step solution

Step 1. Given information

Step 2. Value of determinant

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Discrete Mathematics

Pure Maths

Applied Mathematics

Logic and Functions

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 $|\begin{matrix} x & y & z \\ u & v & w \\ 1 & 2 & 3 \end{matrix}| = 4$
role="math" localid="1647384474767" $|\begin{matrix} x & y & z \\ - 3 & - 6 & - 9 \\ u & v & w \end{matrix}|$