GATE CE 2019 Set 2 — Question 45
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Question
The inverse of the matrix
241332414 is
Correct answer
(C) bmatrix -2 & (4)/(5) & (9)/(5) \ 3 & -(4)/(5) & -(14)/(5) \ -1 & (1)/(5) & (6)/(5) bmatrix
Solution
Let
A=241332414.
1.Calculate the determinant ∣A∣: ∣A∣=2(12−2)−3(16−1)+4(8−3)=2(10)−3(15)+4(5)=20−45+20=−5.
2.Calculate the adjoint matrix adj(A): Cofactors:
C11=10,C12=−15,C13=5C21=−4,C22=4,C23=−1C31=−9,C32=14,C33=−6adj(A)=10−155−44−1−914−6.
3.Calculate the inverse A−1: A−1=∣A∣1adj(A)=−5110−155−44−1−914−6=−23−154−545159−51456.
This matches option (C).
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