How do you solve #2x+3y=-1# and #4x-5y=7# using matrices?
Although the method might seem quite daunting, once the preparation process is mastered, the method itself is surprisingly quick and easy, involving a few simple calculations.
We have the following equations:
First write them as matrices:
Now find the inverse matrix of
Multiply both sides of the matrix equation by the inverse matrix.
Background knowledge... to help with the method above..
A 2 x 2 matrix multiplied by the unit matrix remains unchanged
A matrix multiplied by its inverse gives the unit matrix -
also known as the Identity Matrix.
To find the inverse matrix (
Find the determinant
#(abs(M)) = ad-bc#
#M^-1 = 1/((abs(M)))( ( d,-b),(-c,a))#
(swop a and d and change the signs of b and c, then divide by the determinant.)