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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. 43 (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="1647383304224" $|\begin{matrix} 1 & 2 & 3 \\ u & v & w \\ x & y & z \end{matrix}|$

Short Answer

Expert verified

The value of $|\begin{matrix} 1 & 2 & 3 \\ u & v & w \\ x & y & z \end{matrix}|$ is $- 4$

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

Step by step solution

01

Step 1. Given information

The given determinant is

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

02

Step 2. Solution

On comparing both determinants, it seems that the determinant $|\begin{matrix} 1 & 2 & 3 \\ u & v & w \\ x & y & z \end{matrix}|$ is obtained by interchanging the first and third row of determinant $|\begin{matrix} x & y & z \\ u & v & w \\ 1 & 2 & 3 \end{matrix}|$

Property of determinant state that the value of a determinant changes sign if any two rows are interchanged.

Since $|\begin{matrix} x & y & z \\ u & v & w \\ 1 & 2 & 3 \end{matrix}| = 4$

so the value of determinant $|\begin{matrix} 1 & 2 & 3 \\ u & v & w \\ x & y & z \end{matrix}| = - 4$

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Most popular questions from this chapter

Graph each equation of the system. Then solve the system to find the points of intersection.
$\{\begin{cases} y = x^{2} + 1 \\ y = 4 x + 1 \end{cases}$

In Problems 35鈥�42, graph each system of inequalities by hand.

$\{\begin{cases} x^{2} + y^{2} 鈮� 9 \\ x + y 鈮� 3 \end{cases}$

If the lines that make up a system of two linear equations are coincident, then the system is __________ and the equations are ___________.

The ratio of a to b is $\frac{2}{3}$ . The sum of a and b is $10$ . What is the ratio of $a + b$ to $b - a$ ?

In Problems 23鈥�34, graph each system of linear inequalities by hand. Verify your results using a graphing utility

$\{\begin{cases} x - 4 y 鈮� 4 \\ x - 4 y 鈮� 0 \end{cases}$

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