Maths-1996 -Set I

Q1) Using elementary row transformations, find the inverse of the matrix
A = 4 5
3 4

Ans1) Here
A =
4 5
3 4
and I =
1 0
0 1
Now A = IA
=>
4 5
3 4=1 0
0 1
A=> Applying R1 (1/4)R1
1 5/4
3 4=1/4 0
0 1
A=> Applying R2 R2 – 3R1
1 5/4
0 1/4
=
1/4 0
-3/4 1
A=> Applying R2 4R2
1 5/4
0 1=1/4 0
-3 4
A=> Applying R1 R1 – (5/4)R2
1 0
0 1
=
4 -5
-3 4
AA-1 = 4 -5
-3 4
Q2) For the matrices A and B, verify that (A, B)’ = A’B’ where
A = 1 2
3 4
B = 4 5
1 2
Ans2) Here
A = 1 2
3 4
B = 4 5
1 2= 6 9
16 23= 6 16
9 23
R.H.S. = B’A’ =4 1 1 3 = 6 16 = L.H.S.
5 2 2 4 9 23

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