The inverse of the matrix A=(11313−3−2−4−4)A=\left(\begin{array}{ccc}1 & 1 & 3 \\1 & 3 & -3 \\-2 & -4 & -4\end{array}\ri
Question
The inverse of the matrix A=11−213−43−3−4 is:
A.
3−1.25−0.251−0.25−0.251.5−0.75−0.25
B.
3−1.50−0.251−0.25−0.251.5−0.75−0.25
C.
3−1.25−0.251−0.75−0.251.5−0.25−0.25
D.
3−1.25−0.251−0.25−0.751.5−0.75−0.25
Correct option is A
First, ensure the matrix is invertible by checking det(A)=0.det(A)=12133−11−424=1⋅(3⋅(−4)−1⋅(−4))−1⋅((−4)−(−3)⋅(−2))+3⋅((1⋅(−4)−3⋅(−2)))=1⋅(−12+4)−1⋅(−4−6)+3⋅(−4+6)=−8+10+6=8(Non-zero, so invertible)Find the Adjugate (Adjoint) of ACompute the cofactor matrix and transpose it.Cofactor matrix=−2412−8106−12226Transpose (Adjugate):adj(A)=−241021262−8−126Compute the InverseA−1=det(A)1⋅adj(A)=81⋅−241021262−8−126=−31.250.251.50.750.25−1−1.50.75