How do you solve #2x+3y=1# and #4x5y=7# using matrices?
1 Answer
Explanation:
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.
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We have the following equations:
First write them as matrices:
Now find the inverse matrix of
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Multiply both sides of the matrix equation by the inverse matrix.
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Background knowledge... to help with the method above..
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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)) = adbc# 
#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.)