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+1 vote
6.1k views
in Mathematics by (63.5k points)

Solve system of linear equations, using matrix method,

2x + y + z = 1

x - 2y - z = 3/2

3y - 5z = 9

1 Answer

+2 votes
by (64.8k points)
selected by
 
Best answer

The given system can be written as AX = B, where

Thus, A is non-singular, Therefore, its inverse exists. 

Therefore, the given system is consistent and has a unique solution given by X = A−1B. 

Cofactors of A are 

A11 = 20 + 6 = 26, 

A12 = − (− 10 + 0) = 10, 

A13 = 6 + 0 = 6 

A21 = − (− 5 − 3) = 8, 

A22 = − 10 − 0 = − 10, 

A23 = − (6 − 0) = − 6 

A31 = (− 2 + 4) = 2, 

A32 = − (− 4 − 2) = 6, 

A33 = − 8 − 2 = − 10

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