Determinants Test- 4 Notes - Class 12

Class 12: Determinants Test- 4 Notes - Class 12

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CBSE TEST PAPER-09 
CLASS - XII MATHEMATICS (Algebra) 
Topic:- Determinants
1. If
x      2 6  2
,
18    x 18  6
= than x is equal to   [1] 
2. 
1  2
1  4
A
? ?
=
? ?
? ?
is singular or not [1] 
3. Without expanding, prove that
2 2 3
2 2 3
2 2 3
a     a bc a     a a
b     b ca b     b b
     c ab     c c c c
= [1] 
4. 
2     -3      5
6  0  4 ,
1      5     -7
A = Verify that det A = det ( ') A [1] 
5. Show that using properties of det.
1+a     1  1
1 1 1
1  1+b      1 1
1  1      1+c
abc
a b c
? ?
= + + +
? ?
? ?
 [1] 
abc bc ca ab = + + +
6. If x, y, z are different and 
2 3
2 3
2 3
x      x 1+x
  y 1+y 0
z      z 1+z
y ? = = then show that 1 + xyz = 0  [4] 
7. Find the equation of the line joining A (1, 30 and B (0, 0) using det. Find K if D (K, 0)
is a point such then area of ? ABC is 3 square unit [4] 
8. Show that the matrix
2  3
1  2
A
? ?
=
? ?
? ?
 satisfies the equation A
2
 – 4A + I = 0. 
Using this equation, find A
-1
 [4] 
9. Solve by matrix method. [4] 
3x – 2y + 3z = 8
2x + y – z = 1
4x – 3y + 2z = 4
10. The sum of three no. is 6. Of we multiply third no. by 3 and add second no. to it,
we get II. By adding first and third no. we get double of ht second no. represent it
algebraically and find the no. using matrix method. [4] 
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