Q. 24 Write the system of equations co... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 11: Q. 24 (page 729)

Write the system of equations corresponding to each augmented matrix. Then perform the indicated row operation(s) on the given augmented matrix.
$[\begin{matrix} 4 & - 3 & - 1 | & 2 \\ 3 & - 5 & 2 | & 6 \\ - 3 & - 6 & 4 | & 6 \end{matrix}], R_{1} = - r_{2} + r_{1}, R_{3} = r_{2} + r_{3}$

Short Answer

Expert verified

The resultant matrix is

$[\begin{matrix} 1 & 2 & 1 | & 8 \\ 3 & - 5 & 2 | & 6 \\ 0 & - 11 & 6 | & 12 \end{matrix}]$

Step by step solution

Step 1. Given Information

The given matrix and operation is

$[\begin{matrix} 4 & - 3 & - 1 | & 2 \\ 3 & - 5 & 2 | & 6 \\ - 3 & - 6 & 4 | & 6 \end{matrix}], R_{1} = - r_{2} + r_{1}, R_{3} = r_{2} + r_{3}$

Step 2. Explanation

The given matrix has three rows. So, it represents a system of three linear equations. The 3 columns to the left of vertical bar indicate that the system has three variables.

Let the variables be x, y and z. Then system of linear equation corresponding to the given matrix is as follows,

$4 x - 3 y - z = 2 3 x - 5 y + 2 z = 6 - 3 x - 6 y + 4 z = 6$

Apply the first-row operation on the given augmented matrix and simplify,

$[\begin{matrix} 4 & - 3 & - 1 | & 2 \\ 3 & - 5 & 2 | & 6 \\ - 3 & - 6 & 4 | & 6 \end{matrix}] 鈫� [\begin{matrix} - 3 + 4 & 5 + (- 3) & - 2 + (- 1) | & - 6 + 2 \\ 3 & - 5 & 2 | & 6 \\ - 3 & - 6 & 4 | & 6 \end{matrix}] 鈫� [\begin{matrix} 1 & 2 & 1 | & 8 \\ 3 & - 5 & 2 | & 6 \\ - 3 & - 6 & 4 | & 6 \end{matrix}]$

Now, apply the second-row operation on the given matrix and simplify,

localid="1647504786319" $[\begin{matrix} 1 & 2 & 1 | & 8 \\ 3 & - 5 & 2 | & 6 \\ - 3 & - 6 & 4 | & 6 \end{matrix}] 鈫� [\begin{matrix} 1 & 2 & 1 | & 8 \\ 3 & - 5 & 2 | & 6 \\ 3 + (- 3) & - 5 + (- 6) & 2 + 4 | & 6 + 6 \end{matrix}] 鈫� [\begin{matrix} 1 & 2 & 1 | & 8 \\ 3 & - 5 & 2 | & 6 \\ 0 & - 11 & 6 | & 12 \end{matrix}]$

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91影视

Write the system of equations corresponding to each augmented matrix. Then perform the indicated row operation(s) on the given augmented matrix.
$[\begin{matrix} 4 & - 3 & - 1 | & 2 \\ 3 & - 5 & 2 | & 6 \\ - 3 & - 6 & 4 | & 6 \end{matrix}], R_{1} = - r_{2} + r_{1}, R_{3} = r_{2} + r_{3}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

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91影视

Write the system of equations corresponding to each augmented matrix. Then perform the indicated row operation(s) on the given augmented matrix. 4-3-1|23-52|6-3-64|6,R1=-r2+r1,R3=r2+r3

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

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Most popular questions from this chapter

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Discrete Mathematics

Calculus

Geometry

Applied Mathematics

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Study anywhere. Anytime. Across all devices.

Write the system of equations corresponding to each augmented matrix. Then perform the indicated row operation(s) on the given augmented matrix.
$[\begin{matrix} 4 & - 3 & - 1 | & 2 \\ 3 & - 5 & 2 | & 6 \\ - 3 & - 6 & 4 | & 6 \end{matrix}], R_{1} = - r_{2} + r_{1}, R_{3} = r_{2} + r_{3}$