Solve system of linear equations, using matrix method.

x – y + z = 4


2x + y – 3z = 0


x + y + z = 2


The given system of equations is:

x - y + z = 4


2x + y -3z = 0


x + y + z = 2


The given system of equations can be written in the form of AX = B, where



Now |A| = 1(1+3) + 1(5) + 1(1) = 10 ≠ 0


A is a non-singular matrix and hence A-1 exists.


Now A11 = 4, A12 = -5, A13 = 1, A21 = 2, A22 = 0, A23 = -2, A31 = 1, A32 = -2, A33 = 3


So AdjA =



And hence X = A-1B


So


Hence x = 2, y = -1 and z = 1.


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