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,

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

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

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

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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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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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Theoretical and Mathematical Physics

Calculus

Probability and Statistics

Mechanics Maths

Decision Maths

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