In linear algebra, an augmented matrix is used to represent a system of linear equations. It consists of the coefficients of the variables along with the constants from the right side of the equations aligned in a single matrix.
Given the system of equations:
1. \$x + y = 5\$
2. \$3x - y = -1\$
The coefficients of \$x\$ and \$y\$ from the first equation are 1 and 1, and from the second equation, they are 3 and -1. The constants are 5 and -1. The augmented matrix form for this system would be:
\[
\begin{bmatrix}
1 & 1 & | & 5 \\
3 & -1 & | & -1 \\
\end{bmatrix}
\]
The lines in the augmented matrix separate the coefficients on the left from the constants on the right, similar to how the equal sign separates them in the equations themselves.
what would the following system of equations look like in augmented matrix form?
x + y = 5
3x - y = -1
1 answer