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Solving Equations by Determinants-Cramer’s Rule

If the number of equations is more than two, it is easier to get the solution by using determinants.

If I1,  I 2 and I a are the three unknowns in a system of three linear equations

a11 I 1 + a12I2 + a13I3 = C1

a21I 1 + a22I2 + a23I3 = C2

a31I 1 + a32I2 + a 33I3 = C3

Then, the system can be written in matrix form as follows

The values of I1 and  I2 and I3 are given by

This is known as Cramer’s rule and can be applied to any system of n linear equations provided  Δ is not zero