To start, click the "enter a matrix" button on the right. Then type in matrix operations in the textbox below. Read the help pages by clicking on the link in the upper right corner to read all the operations that can be performed.
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This page provides basic operations on matrices including addition, subtraction, mutiplication and powers as well as determinant and inverses.
In order to start, enter a matrix by clicking on the button "Enter a matrix" on the right side of the page. Type in a name for the matrix in the first box, and the matrix in the second (larger) box. Type each element of the matrix separated by spaces and each row of the matrix should be on a separate line. For example, the matrix: \[ \left[\begin{array}{rrr} 1 & 2 & 3 \\ 4 & 5 & 6 \\7 & 8 & 9 \end{array} \right] \]
Should be entered like:
1 2 3 4 5 6 7 8 9
Once entered, the matrix will appear in the right column. These are the matrices available for use.
A column vector should be entered as a single entry per line. For example, the column vector \[ \left[\begin{array}{r} 1\\ 2 \\3 \end{array} \right]\]
Should be entered like:
1 2 3
Matrices may contain fractional entries. To include a fraction enter it with the "/". For example 1/2 should be entered as "1/2".
The operations of addition, subtraction and multiplication are performed with two matrices and use the symbols: +, -, * respectively. For example, suppose that two matrices called "A" and "B" have been entered. Then "A*B" will return the product.
Scalar multiplication of numbers is also defined. Entering 2*A returns a matrix in which each element of A is mutiplied by two.
Note:Although it is common to leave out the multiplication sign * when writing matrix operations, like AB, you must explicitly put in the multiplication sign.
The square of a matrix is defined as the matrix times itself. Other powers are similarly defined. You can find the cube of a square matrix "A", entering A^3.
As you enter operations on matrices, you will see a line number produced to the right of each output. You can use this. For example if you see \[ B-C = \left[\begin{array}{rr} 4 & -2 \\ -1 & 4 \\ 0 & 0 \end{array}\right] \qquad\qquad[1] \] then you can do another operation using [1]. If you have a compatible matrix \(A\), then A*[1] will produce something like: \[ A(B-C) = \left[\begin{array}{rr} 2&6 \\ 11 & 12 \\ 30 & -8 \end{array}\right] \qquad\qquad[2] \]
The determinant can be found using the function det. If A is a square matrix, then det(A) will return its determinant. Note: the matrix must be square or an error will be generated.
The inverse can be found using the function inv. If A is a square matrix, then inv(A) will return its inverse, if it exists. If not, an error will be shown. An error will also be generated if the matrix is not square.
You can create a new matrix by augmenting (concatenating) two matrices with the same number of rows. If "A" and "B" are the matrix, entering aug(A,B) will return the augmented matrix.
You can produce an \(n \times n\) identity matrix with I(n). For example, a \(4 \times 4\) identity matrix is I(4)
Gauss-Jordon Elimination or row reduction take a matrix and returns a matrix in reduced row echelon form. A matrix is in row echelon form if the leading element in each row (the leading element in a row is the left-most non-zero element) has zeros both below it and to its right. A reduce row echelon form also requires that a leading element is a 1 and it is the only non zero element in its column.
To perform row reduction on a matrix A, type rref(A).
A number of error can occur while using this page. All errors will give a pop up window indicating what is wrong. Here is a list of most possible errors: