Objectives
- Solve systems of linear equations using the method of elimination
- Become more familiar with the terminology and parts of a matrix
- Go back and forth between a linear system and an augmented matrix
Worksheet Participate
Elimination.
Solve the linear systems below using the method of elimination.
1.
\begin{align*}
2x_1 + 4x_2 \amp = -6\\
5x_1 - 5x_2 \amp = 15
\end{align*}
2.
\begin{align*}
x_1 + x_2 - x_3 \amp = 1 \\
x_1+ 2x_2 -x_3 \amp = 2\\
x_2+ x_3 \amp = 3 \\
x_2 - x_4\amp = 4
\end{align*}
Parts of a Matrix.
For the matrix \(B=\left[\begin{array}{cccc} 1\amp 1\amp -1\amp 2\\ 2\amp 1\amp 5\amp 7\\ 0\amp -5\amp -3\amp \frac{1}{2}\\ \end{array} \right]\text{,}\) identify the
3.
entry \(b_{32}\text{.}\)
4.
third column.
5.
second row.
6.
If \(A\) is a \(3\times 5\) matrix, how many columns does \(A\) have?
7.
Using variables \(x_1, x_2, \ldots \text{,}\) write the linear system corresponding to the above matrix \(B\text{.}\)
8.
Give the augmented matrix corresponding to the linear system in 2.
9.
Create your own augmented matrix, of any size you choose.
10.
Create your own linear system, with however many variables and equations you choose.
