Class-12-Math-Assignment-on-Matrices.pdf - Test-3 Marks...

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Test-3 Time- 1.5 hrs. Marks- 12x5 Matrices Q.1. Construct a 3 × 4 matrix, whose elements are given by a ij = j i + - 3 2 1 Q.2. If A = - 6 3 2 4 0 8 and B = - - 1 5 2 4 2 2 , then find the matrix X, such that 2A + 3X = 5B. Q.3. If A = - 0 2 / tan 2 / tan 0 α α and I = 1 0 0 1 , then show that I+A= (I – A) - α α α α cos sin sin cos Q.4. Express the matrix A= - - - - - 3 2 1 4 3 1 4 2 2 as the sum of symmetric & skew-symmetric matrix. Q.5. Obtain the inverse of the matrix A = 1 1 3 3 2 1 2 1 0 using elementary transformations. Q.6. If f(x)= - 1 0 0 0 cos sin 0 sin cos x x x x Prove that f(x). f(y) = f(x + y) Q.7. If A and B are invertible matrices of the same order, then prove that (AB) -1 = B -1 A -1 Q.8. Let f(x) = x 2 – 5x + 6. Find f(A) If A =
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