QuestionChoose the augmented matrix for the system of linear equations. $\left\{\begin{array}{c} 3 x+y+z=0 \\ 10 x-10 z=0 \\ x+10 y+3 z=10 \end{array}\right.$

Studdy Solution

STEP 1

1. The system of linear equations is given and consists of three equations with three variables: $x$ , $y$ , and $z$ .
2. We need to represent this system as an augmented matrix.

STEP 2

1. Identify the coefficients of each variable in the system of equations.
2. Construct the augmented matrix using these coefficients and the constants from the right-hand side of the equations.

STEP 3

Identify the coefficients of each variable in the system of equations:
For the first equation $3x + y + z = 0$ , the coefficients are: - $x$ : 3 - $y$ : 1 - $z$ : 1 - Constant: 0
For the second equation $10x - 10z = 0$ , the coefficients are: - $x$ : 10 - $y$ : 0 (since $y$ is not present) - $z$ : -10 - Constant: 0
For the third equation $x + 10y + 3z = 10$ , the coefficients are: - $x$ : 1 - $y$ : 10 - $z$ : 3 - Constant: 10

STEP 4

Construct the augmented matrix using the coefficients and constants identified:
The augmented matrix is:
$\begin{bmatrix} 3 & 1 & 1 & | & 0 \\ 10 & 0 & -10 & | & 0 \\ 1 & 10 & 3 & | & 10 \end{bmatrix}$
This matrix represents the system of linear equations in augmented form.

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