Download OU B.Sc 2019 Dec 5th Sem (3rd Year) 8187E Mathematics (Linear ALgebra) Question Paper

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Time : 3 Hours

(3x15=45 Marks)

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(Answer Type) Answer all from the questions.

1. (a) Define linear transformation. Let T: M₂ ? M₂ be defined by T(A) = A^T. Show that T is a linear transformation.
2. (b) Find the dimension of the subspace of R⁴ spanned by the vectors:
   v₁ = (1, -4, -2, -1), v₂ = (2, -3, -1, 5), v₃ = (3, -8, -2, 9), v₄ = (3, -7, -3, 4)

OR

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2. (a) Show that if v₁, v₂ ... v_n are linearly independent vectors, then so are v₁, v₁ + v₂, ..., v₁ + v₂ + ... + v_n.
3. (b) Is ? = 3 an eigenvalue of A = [[2, -1, 0], [1, 2, -1], [0, -1, 2]]? If so, find an eigenvector.

3. (a) Diagonalize A = [[3, -2, 0], [-2, 3, 0], [0, 0, 5]]

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