Question

x+y+z = 6
x-y+z = 2
2x-y+3z = 9

Examine whether the given system of equations is consistent or not and if consistent find x,y,z.
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Answer 1

using matrix inversion method

AX=B

⎣⎢⎢⎡211−11−1311⎦⎥⎥⎤ ⎣⎢⎢⎡xyz⎦⎥⎥⎤=⎣⎢⎢⎡962⎦⎥⎥⎤

and X=A−1B where A−1=∣A∣adj(A)

Now adjA=⎣⎢⎢⎡20−2−2−1−1−413⎦⎥⎥⎤

∣A∣=2(1+1)−1(1−1)+3(−1−1)

∣A∣=4−6

∣A∣=−2

Now A−1=