Matrices Test 05 (Class 12, CBSE) Class 12 Notes | EduRev

Class 12 : Matrices Test 05 (Class 12, CBSE) Class 12 Notes | EduRev

 Page 1


CBSE TEST PAPER-05 
CLASS - XII MATHEMATICS (algebra) 
Topic:- Matrices 
1. Show that
0      1     -1
-1     0      1
1     -1      0
A
? ?
? ?
=
? ?
? ?
? ?
, is  skew symmetric matrix. [1] 
2. 
2  4
,
5  6
A
? ?
=
? ?
? ?
Prove that ' A A + is a symmetric matrix [1] 
3. If
-1    5
3  2
A
? ?
=
? ?
? ?
show that ( ) 3 ' 3 ' A A = [1] 
4. Solve for x and y, given that
  y 1 3
3y    x 2 5
x ? ?? ? ? ?
=
? ?? ? ? ?
? ?? ? ? ?
[1] 
5. Given example of matrix A and B such that AB = 0 but A ? 0, B ? 0 [1] 
6. If
cos   sin
-sin   cos
A
? ?
? ?
? ?
=
? ?
? ?
then prove that 
cos n   sin n
-sin n   cos n
n
A
? ?
? ?
? ?
=
? ?
? ?
[4] 
7. Find X and Y, if 2x + 3y =
2  3 2    -2
 3 2
4  0 -1    5
and x y
? ? ? ?
+ =
? ? ? ?
? ? ? ?
[4] 
8. If
2 2
2 2
cos sin cos sin cos cos
 = ,  = 
sin sin cos sin cos sin
A B
a a ß ß a ß
a ß a a ß ß
? ? ? ?
? ? ? ?
? ? ? ?
Show that AB is a zero matrix if a and ß differ by an odd multiple of .
2
p
[4] 
9. If f(x) = x
2
 – 5x + 7  and
3  1
-1   2
A
? ?
=
? ?
? ?
 find  f(A) [4] 
10. 
4  3
,
2  5
A
? ?
=
? ?
? ?
find x and y such that A
2
 – xA + yI = 0 [4] 
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