Inverse of square matrix:
The inverse is, hence the result of multiplying the scalar 1/D by each and every element in the preceding matrix. Note that this is not the matrix A, but is determined by using the elements from A in the manner shown below: the values on the diagonal are reversed, and the operator negation is used on the other two values.
Note that if the determinant D is 0, it will not be possible to find the inverse of the matrix A.
The unknowns are found by evaluating this matrix multiplication, and hence:
x1 = -1 * 2 + 1 * 6 = 4
x2 = 1 * 2 + (-1/2) * 6 = -1
This, obviously, is the similar solution as found by the intersection of the two lines.
To do this in a MATLAB, at first we would generate the coefficient matrix variable a and column vector b.
>> a = [1 2; 2 2];
>> b = [2;6];