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-
→
Rate this question :






















Which of the following statements are True or False
If A, B and C are square matrices of same order, then AB = AC always implies that B = C.
Mathematics - ExemplarWhich of the following statements are True or False
If A, B and C are square matrices of same order, then AB = AC always implies that B = C.
Mathematics - ExemplarUsing matrices solve the following system of equations.
3x + 4y + 7z = 4
2x – y + 3z = –3
x + 2y – 3z = 8
Mathematics - Board PapersUsing matrices, solve the following system of equations:
2x - 3y + 5z = 11
3x + 2y - 4z = -5
x + y - 2z = -3
Mathematics - Board PapersUsing matrices solve the following system of equations:
x + y – z = 3; 2x + 3y + z = 10; 3x – y – 7z = 1
Mathematics - Board PapersIf A is an invertible matrix and A-1 = then A=?
If A=is not invertible then λ=?
Find the adjoint of the matrix and hence show that A(adj A) = |A| I3.