Chapter 2 Matrices
2.5 Matrix Calculator
Learning Objectives
By the end of this section, you should be able to:
- Use a matrix calculator
- to solve systems of equations
- for basic operations
- to solve systems with inverses
In Sections 2.2 through 2.4, you learned how to solve systems using matrices, perform basic matrix operations, and solve systems with inverses by hand. There are many resources that can be used to perform different matrix operations. One free resource is the Desmos Matrix Calculator. You can use the link to open a new webpage with the calculator or use the calculator that is located in the Back Matter of this textbook.
To create a matrix in the matrix calculator,
- Click the [latex]\begin{array}{|c|}\hline \text{New Matrix}\\ \hline \end{array}\;[/latex] button.
- Define the size of the matrix using the [latex]\begin{array}{|c|}\hline -\\ \hline \end{array}\;[/latex] and [latex]\begin{array}{|c|}\hline +\\ \hline \end{array}\;[/latex] buttons next to Row and Column.
- Fill in the elements of the matrix.
The matrix calculator is useful in finding row-echelon form, performing basic operations, and solving systems with inverses.
Reduced Row-Echelon Form
In Section 2.2, we worked problems where we found row-echelon form by hand. When using a matrix calculator, you can find the reduced row-echelon form, which can help you solve systems of equations. The reduced row-echelon is similar to row-echelon form, but the ones in the main diagonal are the only nonzero numbers in each column. To find the reduced row-echelon form in the matrix calculator,
- Create a matrix.
- Click the [latex]\begin{array}{|c|}\hline \text{rref}\\ \hline \end{array}\;[/latex][latex]\begin{array}{|c|}\hline \text{A}\\ \hline \end{array}\;[/latex].
- Note that if you created more than one matrix, you will have to choose the appropriate letter based on what you named the matrix. So, if you want to find the reduced echelon form of matrix C, you’ll click [latex]\begin{array}{|c|}\hline \text{rref}\\ \hline \end{array}\;[/latex][latex]\begin{array}{|c|}\hline \text{C}\\ \hline \end{array}\;[/latex].
Examples from Section 2.2
Only the Examples that involve solving systems
Solve the given system by Gaussian elimination.
[latex]\begin{cases}2x+3y=6\\x-y=\frac{1}{2}\end {cases}[/latex]
First we write this as an augmented matrix.
[latex]\left[ \begin{array}{cc|c} 2&3&6\\1&-1&\frac{1}{2} \end{array} \right ][/latex]
Create matrix A in the calculator by clicking [latex]\begin{array}{|c|}\hline \text{New Matrix}\\ \hline \end{array}\;[/latex]. The augmented matrix is a [latex]2 \times 3[/latex] matrix, so add one column to matrix A, and fill in the entries. Note that the vertical line of the augmented matrix will not be in matrix A in the calculator.
Click [latex]\begin{array}{|c|}\hline \text{rref}\\ \hline \end{array}\;[/latex][latex]\begin{array}{|c|}\hline \text{A}\\ \hline \end{array}\;[/latex], and the calculator will find the row-echelon form of the matrix. By clic