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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 11: Q.32 (page 794)

In Problems $32$ and $33$ , use properties of determinants to find the value of each determinant if it is known that $|\begin{matrix} x & y \\ a & b \end{matrix}| = 8$
$|\begin{matrix} 2 x & y \\ 2 a & b \end{matrix}|$

Short Answer

Expert verified

If $|\begin{matrix} x & y \\ a & b \end{matrix}| = 8$ , then the value of the determinant $|\begin{matrix} 2 x & y \\ 2 a & b \end{matrix}|$ is $16$

Step by step solution

01

Step 1. Given data

The given determinant is

$|\begin{matrix} x & y \\ a & b \end{matrix}| = 8$

The value of determinant need to find out is

role="math" localid="1646934897550" $|\begin{matrix} 2 x & y \\ 2 a & b \end{matrix}|$

02

Step 2. Value of determinant

According to properties of determinants, if $|\begin{matrix} l & m \\ n & o \end{matrix}| = p$

then $|\begin{matrix} k l & m \\ k n & o \end{matrix}| = k p$

So

$|\begin{matrix} 2 x & y \\ 2 a & b \end{matrix}| = 2 (8) |\begin{matrix} 2 x & y \\ 2 a & b \end{matrix}| = 16$

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Most popular questions from this chapter

Solve each system of equations. If the system has no solution, say that it is inconsistent.

$\{\begin{matrix} 2 x + y = 1 \\ 4 x + 2 y = 3 \end{matrix}$

Verify that the values of the variables listed are solutions of the system of equations.

$\{\begin{matrix} 2 x + \frac{1}{2} y = 0 \\ 3 x - 4 y = - \frac{19}{2} \end{matrix} x = - \frac{1}{2}, y = 2; (- \frac{1}{2}, 2)$

Verify that the values of the variables listed are solutions of the system of equations.

$\{\begin{matrix} 3 x - 4 y = 4 \\ \frac{1}{2} x - 3 y = - \frac{1}{2} \end{matrix} x = 2, y = \frac{1}{2}; (2, \frac{1}{2})$

Solve each system of equations. If the system has no solution, say that it is inconsistent.

$2 x - 3 y - z = 0 3 x + 2 y + 2 z = 2 x + 5 y + 3 z = 2$

The difference of two numbers is the same as their product, and the sum of their reciprocals is $5$ . Find the numbers.

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