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Matrices

The matrices section of QuickMath allows you to perform arithmetic operations on matrices. Currently you can add or subtract matrices, multiply two matrices, multiply a matrix by a scalar and raise a matrix to any power.

What is a matrix?

A matrix is a rectangular array of elements (usually called scalars), which are set out in rows and columns. They have many uses in mathematics, including the transformation of coordinates and the solution of linear systems of equations.

Here is an example of a 2x3 matrix :

1   2   3

4   5   6

Arithmetic

The arithmetic suite of commands allows you to add or subtract matrices, carry out matrix multiplication and scalar multiplication and raise a matrix to any power.

Matrices are added to and subtracted from one another element by element. For instance, when adding two matrices A and B, the element at row i, column j of A is added to the element at row i, column j of B to give the element at row i, column j of the answer. Consequently, you can only add and subtract matrices which are the same size.

Matrix multiplication is a little more complicated. Suppose two matrices A and B are multiplied together to get a third matrix C. The element at row i, column j in C is found by taking row i from A and multiplying it by column j from B. Two matrices can only be multiplied together if the number of columns in the first equals the number of rows in the second.

Multiplying a matrix by a scalar simply involves multiplying each element by that scalar, whilst raising a matrix to a positive integer power can be achieved by a series of matrix multiplications.

There is currently no advanced arithmetic section, though this may be introduced in the future.

Go to the Arithmetic page

Inverse

The inverse command allows you to find the inverse of any non-singular, square matrix. The inverse of a square matrix A is another matrix B of the same size such that

A B = B A = I

where I is the identity matrix. The inverse of A is commonly written as A-1.

Go to the Inverse page

Determinant

The determinant command allows you to find the determinant of any non-singular, square matrix.

For example, if A is a 3 x 3 matrix, then its determinant can be found as follows :

det(A) = a1,1 A1,1 - a1,2 A1,2 + a1,3 A1,3

where ai,j is the element of A at row i, column j and Ai,j is the matrix constructed from A by removing row i and column j.

Go to the Determinant page

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