College Algebra - Systems of Equations

Use augmented matrices to solve the following system of equations:

Suppose you are trying to solve a system of three linear equations in three variables using the Gauss-Jordan elimination method on an augmented matrix. After a row operation, the matrix that appears is

$\begin{bmatrix}1 & -5 & 3\0 & 0 & 0 \0 & 0 & 0 \ \end{matrix}$ $\begin{vmatrix}-8 \0 \7\end{bmatrix}$

How many solutions does the system have?

Solve the following Augmented Matrix.

$\begin{bmatrix} 2 & 3 &1 \ 3& 2& 10\ \end{bmatrix}$

$\begin{bmatrix}1 & 0 & 3\0 & 1 & -5 \0 & 0 & 0 \ \end{matrix}$ $\begin{vmatrix}6 \7 \0\end{bmatrix}$

How many solutions does the system have?

Use augmented matrices to solve the following system of equations:

Suppose you are trying to solve a system of two linear equations in two variables using the Gauss-Jordan elimination method on an augmented matrix. After a row operation, the matrix that appears is

$\begin{bmatrix}1 & 8 \0 & 0 \ \end{matrix}$ $\begin{vmatrix}7 \0 \ \end{bmatrix}$

How many solutions does the system have?

Write the augmented matrix for the system of equations given below and perform row operations until the augmented matrix is in row reduced echelon form, then read off the solution.

Note that interchanging rows in a matrix does not change the solution so check for interchanged rows if you don't see your augmented matrix among the augmented multiple choices.

Solve for x, y, and z.

$\begin{bmatrix} 2 &3 &-3 \ 1& 2& 5\ 0&0 & 1 \end{bmatrix}$ $\begin{bmatrix} x\ y\ z \end{bmatrix}=$ $\begin{bmatrix} 3\ 2 \ 1 \end{bmatrix}$

Suppose you are trying to solve a system of two linear equations in two variables using the Gauss-Jordan elimination method on an augmented matrix. After a row operation, the matrix that appears is

$\begin{bmatrix}1 & 0 \0 & 1 \ \end{matrix}$ $\begin{vmatrix}1\-1 \ \end{bmatrix}$

How many solutions does the system have?

When solving a system of three linear equations in three variables using the Gauss-Jordan elimination method, your initial augmented matrix is as follows:

$\begin{bmatrix}-3 & 2& 3 \2 & 4 & -3 \-5 & 2 & 4 \ \end{matrix}$ $\begin{vmatrix}5 \0 \2 \ \end{bmatrix}$

Which of the following is notation for the next step you should perform?

Systems of Equations

Practice Questions