Q. 44.1( 27 Votes )
Using elementary transformations, find the inverse of each of the matrices.
Answer :
First of all we need to check whether the matrix is invertible or not. For that-
For the inverse of a matrix A to exist,
Determinant of A ≠ 0
Here ∣A∣ = (2)(7) – (5)(3) = -1
So the matrix is invertible.
Now to find the inverse of the matrix,
We know AA-1 = I
Let’s make augmented matrix-
→ [ A : I ]
→
Apply row operation- R2→ R2 – 
R1
→ 
Apply row operation- R1→ R1/2
→
Apply row operation- R1→ R1 + 3R2
→
Apply row operation- R2→ -2R2
→
The matrix so obtained is of the form –
→ [I : A-1]
Hence inverse of the given matrix-
→ 
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