Question

(ii) x+y+z=6, 3x - y + 3z = 10, 5x + 5y - 4z = 3.
[Find A using adjoint method.]​

Answer 1

Solution:

LetA=⎡⎣⎢1351−1513−4⎤⎦⎥,B=⎡⎣⎢6103⎤⎦⎥,X=⎡⎣⎢xyz⎤⎦⎥

|A|=∣∣∣∣1351−1513−4∣∣∣∣

|A|=1(4−15)−1(−12−15)+1(15+5)

∴|A|=36≠0

∴A−1exists

Matrixofminors=[−11−2720−9−9040−4]

Matrixofcofactors=[−1127209−9040−4]

[xyz]=136[−119427−90200−4][6103]

∴X=A−1B

[xyz]=136[3672108]=[123]