Solve system of linear equations, using matrix method.


The given system of equations is:

2x + y + z = 1



0x + 3y - 5z = 9


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



Now |A| = 2(10+3)-1(-5) +1(3) = 34 ≠ 0


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


Now A11 = 13, A12 = 5, A13 = 3, A21 = 8, A22 = -10, A23 = -6, A31 = 1, A32 = 3, A33 = -5


So AdjA =



And hence X = A-1B


So


Hence


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