Chapter 4: Q. 379 (page 482)

Write the system of equations that corresponds to the augmented matrix.
$[\begin{array}{r} 1 & 0 & - 3 & - 1 \\ 1 & - 2 & 0 & - 2 \\ 0 & - 1 & 2 & 3 \end{array}]$

Short Answer

Expert verified

For the augmented matrix $[\begin{array}{r} 1 & 0 & - 3 & - 1 \\ 1 & - 2 & 0 & - 2 \\ 0 & - 1 & 2 & 3 \end{array}]$ , the system of equations is $\{\begin{cases} x - 3 z = - 1 \\ x - 2 y = - 2 \\ - y + 2 z = 3 \end{cases}$

Step by step solution

Step 1. Given Information

Consider the augmented matrix $[\begin{array}{r} 1 & 0 & - 3 & - 1 \\ 1 & - 2 & 0 & - 2 \\ 0 & - 1 & 2 & 3 \end{array}]$ .

We need to find the corresponding system of equations.

Step 2. Form the system of equations

We remember that each row corresponds to an equation and that each entry is a coefficient of a variable or the constant. The vertical line replaces the equal sign. Since this matrix is a $4 \times 3$ , we know it will translate into a system of three equations with three variables. Thus the corresponding system of equations is

$[\begin{array}{r} 1 & 0 & - 3 & - 1 \\ 1 & - 2 & 0 & - 2 \\ 0 & - 1 & 2 & 3 \end{array}] \to \{\begin{cases} 1 \cdot x + 0 \cdot y + (- 3) \cdot z = - 1 \\ 1 \cdot x + (- 2) \cdot y + 0 \cdot z = - 2 \\ 0 \cdot x + (- 1) \cdot y + 2 \cdot z = 3 \end{cases} \to \{\begin{cases} x - 3 z = - 1 \\ x - 2 y = - 2 \\ - y + 2 z = 3 \end{cases}$

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Write the system of equations that corresponds to the augmented matrix.
$[\begin{array}{r} 1 & 0 & - 3 & - 1 \\ 1 & - 2 & 0 & - 2 \\ 0 & - 1 & 2 & 3 \end{array}]$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Form the system of equations

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Write the system of equations that corresponds to the augmented matrix. 10-3-11-20-20-123

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Form the system of equations

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

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Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

Write the system of equations that corresponds to the augmented matrix.
$[\begin{array}{r} 1 & 0 & - 3 & - 1 \\ 1 & - 2 & 0 & - 2 \\ 0 & - 1 & 2 & 3 \end{array}]$