Chapter 11: Q 14. (page 729)

Write the augmented matrix of the given system of equations.
$\{\begin{cases} 2 x + 3 y - 4 z = 0 \\ x - 5 z + 2 = 0 \\ x + 2 y - 3 z = - 2 \end{cases}$

Short Answer

Expert verified

The solution is $[\begin{matrix} 2 & 3 & - 4 \\ 1 & 0 & 5 \\ 1 & 2 & - 3 \end{matrix} \begin{matrix} | \\ | \\ | \end{matrix} \begin{matrix} 0 \\ - 2 \\ - 2 \end{matrix}]$ .

Step by step solution

Step 1. Given information.

The given system of equations is $\{\begin{cases} 2 x + 3 y - 4 z = 0 \\ x - 5 z + 2 = 0 \\ x + 2 y - 3 z = - 2 \end{cases}$ .

Step 2. Rewrite the system putting the coefficient of the missing variable as zero.

The required equations are $\{\begin{cases} 2 x + 3 y - 4 z = 0 \\ x + 0 \cdot y - 5 z = - 2 \\ x + 2 y - 3 z = - 2 \end{cases}$ .

Step 3. Determine the augmented matrix.

An augmented matrix is used to represent a system of linear equations.

For writing an augmented matrix, the variables of each equation in the system of equations must be on the left side of equal sign and constants on the right side.

A variable that does not appear in the equation has a coefficient zero.

Hence, the required augmented matrix is $[\begin{matrix} 2 & 3 & - 4 \\ 1 & 0 & 5 \\ 1 & 2 & - 3 \end{matrix} \begin{matrix} | \\ | \\ | \end{matrix} \begin{matrix} 0 \\ - 2 \\ - 2 \end{matrix}]$ .

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Write the augmented matrix of the given system of equations.
$\{\begin{cases} 2 x + 3 y - 4 z = 0 \\ x - 5 z + 2 = 0 \\ x + 2 y - 3 z = - 2 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Rewrite the system putting the coefficient of the missing variable as zero.

Step 3. Determine the augmented matrix.

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Write the augmented matrix of the given system of equations.2x+3y-4z=0x-5z+2=0x+2y-3z=-2

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Rewrite the system putting the coefficient of the missing variable as zero.

Step 3. Determine the augmented matrix.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Geometry

Applied Mathematics

Mechanics Maths

Statistics

Calculus

Study anywhere. Anytime. Across all devices.

Write the augmented matrix of the given system of equations.
$\{\begin{cases} 2 x + 3 y - 4 z = 0 \\ x - 5 z + 2 = 0 \\ x + 2 y - 3 z = - 2 \end{cases}$