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Important Questions

CBSE Guess > Papers > Important Questions > Class XII > 2009 > Maths > Mathematics By Mr. Aravind

CBSE CLASS XII

Q. 1. Determine value without expansion

Q. 2. A = Prove that (aI + bA) = anI + nan-1bA for all n values N

Q. 3. A = satisfies and hence solve

2x – 3y = -1
3x+ 4y = 7

Q. 4. Prove that A = is invertible

Q. 5. Prove that

3x + 2y + z =6
4x + 3y + 2z = 9 Has a solution
8x + 16y + y = 25

Q. 6. (a). = xyz(x - y) (y - z) (x - z)

b) A = Find A using ET

Q. 7. Does exist within R ? Justify your answer

* =

Q. 8. (a). An amount of Rs.5000/- is invested in 3 different rates of interests 6%,7%,8% respectively. The total annual income is Rs.358/- and the combined income of the 1st two investments is Rs.70/- more than the 3rd. Find each investment using Matrix Method

(b). Show using properties of determinants

= 2

Q. 9. (a). Show using properties

(b). A = ; B = Find (AB) and

Q. 10. Prove A = is invertible AA-1 is I3

Q. 11. (a). Find A adjA in the following

  1. = A ;
  2. A=

Q. 12. A and B are symmetric prove that :

  1. AB+BA is symmetric
  2. B’AB is symmetric
  3. (A+B)’ is symmetric

Q. 13. Solve using Matrix equations:

3x + y + z = 2
2x - 4y = 3z =-1
4x + y - 3z =-11

Q. 14.Suppose A is a square matrix of order 4. We multiply the matrix by a scalar .Express the determinant of that matrix in terms of the scalar

Q. 15. A = and A+A’ = I find the value of

Q. 16. Inverse of a Matrix using Elementary transformations:

Q. 17. Show using properties of determinants that:

Q. 18. Show that this determinant is independent of 0.

Paper By Mr. Aravind