The system of equations 3 −2 15 −8 92 1 axyz=b3−1 has no solution if a and b are
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a
a=−3,b≠1/3
b
a=2/3,b≠1/3
c
a≠1/4,b=1/3
d
a≠−3,b≠1/3
answer is A.
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Detailed Solution
The augmented matrix is given by(A∣B)=3 −2 1 b5 −8 9 32 1 a −1Applying R1→2R1−R2, we get(A∣B)~14−72b−35−89321a−1Applying R2→R2−5R1,R3→R3−2R1, we get(A∣B)~14−72b−30−284418−10b0−7a+145−4bThe system of equations will have no solution If−28−7=44a+14≠18−10b5−4b⇒ a+14=11 and 20−16b≠18−10b⇒ a=−3 and b≠−1/3