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Q2) Express the matrix
A = 3 1
-4 -1
as the sum of a symmetric and a skew symmetric matrix.
Ans2) We know for a square matrix A. 1/2(A + A’ ) is sym and 1/2(A - A’ ) is skew-symmetric. Also
A = 1/2 (A + A’ ) + 1/2 (A - A’ )
Now
A =
3 1
-4 -1
=>A’ =
3 -4
1 -1
… 1/2 (A + A’ ) = 1/2
6 -3
-3 -2
1/2(A - A’ ) = 1/2
0 5
-5 0
Thus A =
0 -3/2
-3/2 -1
+
0 5/2
-5/2 0
where first one is symmetric and the second skew symmetric
Q3) Evaluate
lim
x->/2 (2x - )/cos x
Ans3)
lim
x->/2 (2x - )/cos x putting /2 - x = , as x -> /2 , -> 0
= lim
->0 (2(/2 - ) - )/cos (/2 - )
= lim
->0
-2/sin = -2 (as lim /Sin = 1)
->0
Pages: 1 2 3 4
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