Question

2x-y+3z=9,x+y+z=6,x-y+z=3 ​

Answer 1

ANSWER

Given

2x−y+3z=9 ………..(1)

x+y+z=6 …………..(2)

x−y+z=2 …………….(3)

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=2−1⎣⎢⎢⎡20−2−2−1−1−413⎦⎥⎥⎤

Now X=A−1B

⎣⎢⎢⎡xyz⎦⎥⎥⎤=2−1⎣⎢⎢⎡20−2−2−1−1−413⎦⎥⎥⎤⎣⎢⎢⎡962⎦⎥⎥⎤

⎣⎢⎢⎡xy