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Matrices : Inverse

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Description

The inverse command in the matrices section of QuickMath allows you to find the inverse of any non-singular, square matrix.

A non-singular matrix is one which has a non-zero determinant, whilst a square matrix is one which has the same number of rows and columns.

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.

To use the inverse command, simply go to the inverse page, type in your matrix and hit the "Inverse" button. Your question will be automatically answered by computer and the reply will be shown in your browser within a few seconds. The answer will be given in two forms : a 'natural' form, which mimics the row and column layout normally used for matrices, and an 'input' form, which is the form required for the entry of matrices into QuickMath. The input form of a solution can be copied and pasted into a matrix input field, so you can use the result from one calculation in another calculation without having to re-type it.

Examples

Here are some examples illustrating the types of matrices you can use the inverse command on and the results which QuickMath will return.

Matrix Result
a, b
c, d
     d                   b
------------      -(------------)
-(b c) + a d        -(b c) + a d

       c               a
-(------------)   ------------
  -(b c) + a d    -(b c) + a d 
1, 2
3, 4
-2     1

3        1
-      -(-)
2        2 
5, 7, 3, 4
8, 9, 2, 3
1, 5, 3, 8
3, 6, 9, 0
157               47      3
---             -(--)   -(-)
12      -7        12      2

  44            13      5
-(--)           --      -
  3     8       3       3

65                19      1
--              -(--)   -(-)
12      -3        12      2

11                3       2
--              -(-)    -(-)
2       -3        2       3