Q 206 Use Row Operations on a Matrix I... [FREE SOLUTION]

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Intermediate Algebra

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OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 4: Q 206 (page 443)

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

Short Answer

Expert verified

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

Part (b) The required matrix is $[\begin{matrix} 4 & - 12 & - 8 & 16 \\ 2 & 2 & - 1 & - 3 \\ 4 & - 2 & - 3 & - 1 \end{matrix}]$

Part (c) The required matrix is $[\begin{array}{r} 1 & - 3 & - 2 & 4 \\ 2 & 2 & - 1 & - 3 \\ 0 & - 6 & - 1 & 5 \end{array}]$

Step by step solution

Part (a) Step 1. Calculating Values

A matrix is given as

[\begin{array}{r} 1 & - 3 & - 2 & 4 \\ 2 & 2 & - 1 & - 3 \\ 4 & - 2 & - 3 & - 1 \end{array}]

Apply given operation as-

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

Part (b) Step 1. Explanation

A matrix is given as

$[\begin{array}{r} 1 & - 3 & - 2 & 4 \\ 2 & 2 & - 1 & - 3 \\ 4 & - 2 & - 3 & - 1 \end{array}]$

Apply given operation as-

$[\begin{array}{r} 1 & - 3 & - 2 & 4 \\ 2 & 2 & - 1 & - 3 \\ 4 & - 2 & - 3 & - 1 \end{array}] \overset{4 R_{1}}{鉄�} [\begin{matrix} 4 脳 1 & 4 (- 3) & 4 (- 2) & 4 脳 4 \\ 2 & 2 & - 1 & - 3 \\ 4 & - 2 & - 3 & - 1 \end{matrix}] \overset{4 R_{1}}{鉄�} [\begin{matrix} 4 & - 12 & - 8 & 16 \\ 2 & 2 & - 1 & - 3 \\ 4 & - 2 & - 3 & - 1 \end{matrix}]$

Part (c) Step 1. Explanation

A matrix is given as

$[\begin{array}{r} 1 & - 3 & - 2 & 4 \\ 2 & 2 & - 1 & - 3 \\ 4 & - 2 & - 3 & - 1 \end{array}]$

Apply given operation as-

$[\begin{array}{r} 1 & - 3 & - 2 & 4 \\ 2 & 2 & - 1 & - 3 \\ 4 & - 2 & - 3 & - 1 \end{array}] \overset{- 2 R_{2} + R_{1}}{鉄�} [\begin{array}{l} 1 & - 3 & - 2 & 4 \\ 2 & 2 & - 1 & - 3 \\ (- 2 脳 2) + 4 & (- 2 脳 2) - 2 & (- 2 脳 (- 1)) - 3 & (- 2 脳 (- 3)) - 1 \end{array}] \overset{- 2 R_{2} + R_{1}}{鉄�} [\begin{array}{r} 1 & - 3 & - 2 & 4 \\ 2 & 2 & - 1 & - 3 \\ 0 & - 6 & - 1 & 5 \end{array}]$

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Short Answer

Step by step solution

Part (a) Step 1. Calculating Values

Part (b) Step 1. Explanation

Part (c) Step 1. Explanation

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91影视

Use Row Operations on a Matrix In the following exercises, perform the indicated operations on the augmented matrices.1-3-2422-1-34-2-3-1鈸� Interchange rows 2and 3鈸� Multiply row 1by 4鈸� Multiply row 2by -2and add to row 3.

Short Answer

Step by step solution

Part (a) Step 1. Calculating Values

Part (b) Step 1. Explanation

Part (c) Step 1. Explanation

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

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Calculus

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Probability and Statistics

Decision Maths

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