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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 4: Q 204 (page 443)

Use Row Operations on a Matrix
In the following exercises, perform the indicated operations on the augmented matrices.
$[\begin{array}{l} 6 & - 4 & 3 \\ 3 & - 2 & 1 \end{array}]$
a Interchange rows $1$ and $2$
b Multiply row $2$ by $3$
c Multiply row $2$ by $- 2$ and add
to row $1$ .

Short Answer

Expert verified

Part (a) The required matrix is $[\begin{array}{l} 3 & - 2 & 1 \\ 6 & - 4 & 3 \end{array}]$

Part (b) The required matrix is $[\begin{array}{l} 6 & - 4 & 3 \\ 9 & - 6 & 3 \end{array}]$

Part (c) The required matrix is $[\begin{matrix} 0 & 0 & 1 \\ 3 & - 2 & 1 \end{matrix}]$

Step by step solution

01

Part (a) Step 1. Explanation

A matrix is given as $[\begin{array}{l} 6 & - 4 & 3 \\ 3 & - 2 & 1 \end{array}]$

$[\begin{array}{r} 6 & - 4 & 3 \\ 3 & - 2 & 1 \end{array}] \overset{R_{1} 鈫� R_{2}}{鉄�} [\begin{array}{r} 3 & - 2 & 1 \\ 6 & - 4 & 3 \end{array}]$

02

Part (b) Step 1. Explanation

A matrix is given as

Apply given operation as-

$[\begin{array}{l} 6 & - 4 & 3 \\ 3 & - 2 & 1 \end{array}] \overset{3 R_{2}}{鉄�} [\begin{array}{l} 6 & - 4 & 3 \\ 9 & - 6 & 3 \end{array}]$

03

Part (c) Step 1. Explanation

A matrix is given as $[\begin{array}{l} 6 & - 4 & 3 \\ 3 & - 2 & 1 \end{array}]$

Apply given operation as-

$[\begin{matrix} 6 & - 4 & 3 \\ 3 & - 2 & 1 \end{matrix}] \overset{- 2 R_{2} + R_{1}}{鉄�} [\begin{matrix} (- 2 路 3) + 6 & (- 2 路 (- 2)) - 4 & (- 2 路 1) + 3 \\ 3 & - 2 & 1 \end{matrix}] \overset{- 2 R_{2} + R_{1}}{鈫�} [\begin{matrix} 0 & 0 & 1 \\ 3 & - 2 & 1 \end{matrix}]$

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Most popular questions from this chapter

The sum of two number is $15$ . One number is $3$ less than the other. Find the numbers.

Solve the system of equations $\{\begin{cases} x + y = 10 \\ x - y = 6 \end{cases}$ (a) by graphing (b) by substitution (c) Which method do you prefer? Why?

In a system of linear equations, the two equations have the same intercepts. Describe the possible solutions to the system.

Without graphing, determine the number of solutions and then classify the system of equations.

$\{\begin{cases} y = \frac{2}{3} x + 1 \\ - 2 x + 3 y = 5 \end{cases}$

Without graphing, determine the number of solutions and then classify the system of equations.

$y = - \frac{1}{2} x + 5 x + 2 y = 10$

See all solutions

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