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CBSE CLASS XII

Matrices

Q. 1. Construct a 3´4 matrix, whose elements are given by aij=

Q. 2. If A = and B = , then find the matrix X, such that 2A + 3X = 5B.

Q. 3. If A = and I = , then show that I+A= (I – A)
Q. 4. Express the matrix A= as the sum of symmetric and skew-symmetric matrix
Q. 5. Obtain the inverse of the matrix A = using elementary transformations.

Q. 6. If f(x)= Prove that f(x). f(y) = f(x + y)

Q. 7. Show that the matrix B¢AB is symmetric or skew-symmetric according as A is symmetric or skew symmetric.

Q. 8. If A and B are invertible matrices of the same order, then prove that (AB)^-1 = B-1A^-1
Q. 9. Let f(x) = x² – 5x + 6. Find f(A) If  A =
Q. 10. If A = Show that A² -5A + 7I = 0, Use this to find A⁴.
Q. 11. Express the matrix A = as the sum of a symmetric and a skew-symmetric matrix.
Q. 12. Find the values of x, y, z if the matrix A = satisfy the equation A¢A = I3.

Q. 13. Show that: =

Q. 14. Show that the following system of equations is consistent 2x – y + 3z = 5, 3x + 2y – z = 7, 4x + 5y – 5z = 9 Also, find the solution.

Prepared By Anil Kumar Tondak
M.Sc.(Maths), M.Ed., M.A.(Eco),M.B.A.(Mkt)
Mob No. 9811363962