Solve simultaneous equations by using matrix method?

watch this video lecture by me you will know how to solve it

http://www.youtube.com/watch?v=ytlZMDs3GeA

I don't know. I think the people before me might have needlessly overcomplicated things.
I'd just use Cramer's rule.

The determinant of the (a) system is
| 2 2 |
| 4 3 | = 2*3 - 4*2 = -2 (Thus it does have a solution)

The x-determinant of the system is (just switch the coefficients of x with the right-hand sides'):
| 2 2 |
| 7 3 | = 2*3 - 7*2 = -8

The y-determinant is:
| 2 2 |
| 4 7 | = 2*7 - 4*2 = 6

The solution is thus: det(x)/det(system), det(y)/det(system)
Or, rather: 4, -3

Inverse of a Matrix
Matrix Inverse
Multiplicative Inverse of a Matrix

For a square matrix A, the inverse is written A-1. When A is multiplied by A-1 the result is the identity matrix I. Non-square matrices do not have inverses.

Note: Not all square matrices have inverses. A square matrix which has an inverse is called invertible or nonsingular, and a square matrix without an inverse is called noninvertible or singular.



AA-1 = A-1A = I

Example: For matrix , its inverse is since

AA-1 =

and A-1A = .




Here are three ways to find the inverse of a matrix:

1. Shortcut for 2x2 matrices

For , the inverse can be found using this formula:



Example:

2. Augmented matrix method

Use Gauss-Jordan elimination to transform [ A | I ] into [ I | A-1 ].

Example: The following steps result in .



so we see that .

3. Adjoint method

A-1 = (adjoint of A) or A-1 = (cofactor matrix of A)T

Example: The following steps result in A-1 for .

The cofactor matrix for A is , so the adjoint is . Since det A = 22, we get

.




See also

Determinant of a matrix, cofactor