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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. 16 (page 793)

In Problems 13鈥�16, use the following matrices to compute each expression.
$A = [\begin{matrix} 1 & 0 \\ 2 & 4 \\ - 1 & 2 \end{matrix}] B = [\begin{matrix} 4 & - 3 & 0 \\ 1 & 1 & - 2 \end{matrix}] C = [\begin{matrix} 3 & - 4 \\ 1 & 5 \\ 5 & 2 \end{matrix}]$
$B C$

Short Answer

Expert verified

$B C = [\begin{matrix} 9 & - 31 \\ - 6 & - 3 \end{matrix}]$

Step by step solution

01

Step 1. Given information

The given matrices are

$A = [\begin{matrix} 1 & 0 \\ 2 & 4 \\ - 1 & 2 \end{matrix}] B = [\begin{matrix} 4 & - 3 & 0 \\ 1 & 1 & - 2 \end{matrix}] C = [\begin{matrix} 3 & - 4 \\ 1 & 5 \\ 5 & 2 \end{matrix}]$

02

Step 2. Find the value of expression BC.

$B C = [\begin{matrix} 4 & - 3 & 0 \\ 1 & 1 & - 2 \end{matrix}] [\begin{matrix} 3 & - 4 \\ 1 & 5 \\ 5 & 2 \end{matrix}] = [\begin{matrix} 4 路 3 + (- 3) 路 1 + 0 路 5 & 4 路 (- 4) + (- 3) 路 5 + 0 路 2 \\ 1 路 3 + 1 路 1 + (- 2) 路 5 & 1 路 (- 4) + 1 路 5 + (- 2) 路 2 \end{matrix}] = [\begin{matrix} 9 & - 31 \\ - 6 & - 3 \end{matrix}]$

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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.

$x - y = 6 2 x - 3 z = 16 2 y + z = 4$

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

$\{\begin{matrix} \begin{array}{rcl} 4 x - 5 z & = & 6 \\ 5 y - z & = & - 17 \end{array} \\ - x - 6 y + 5 z = 24 \end{matrix} x = 4, y = - 3, z = 2; (4, - 3, 2)$

The sum of two numbers is the same as their product, and the difference of their reciprocals is $3$ . Find the numbers.

Graph each equation of the system. Then solve the system to find the points of intersection.

$\{\begin{cases} y = x^{2} + 1 \\ y = x + 1 \end{cases}$

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

$\{\begin{cases} x + 4 y 鈮� 8 \\ x + 4 y 鈮� 4 \end{cases}$

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