Mathematics for computing-1 — DU B. Voc – Software Development Previous Year Question Papers

5 vector fie ld (a) Find the divergence and curl of (b) What is positive definite matrix? Is the following matrix positive definite? (g) 6 (a) Find the eigen values and vectors for the following matrix A : e) (b) Show that the following matrix is diagonalizable: (a) Determine if the following set of vectors are linearly independent or independent : (7) (b) Prove that the vectors i = 2t+ 4j + 6it,j = 6i- a1 *rp and, 2 = 2i- 12j - 10[ form a linearly dependent sysrem. e63i ) Nurn" of the Course : Bachelors of Vocation ((Software Development) Each question is of 5 marks. (a) Find the value of y for which the given and (3, -5, 7y) are vectors linearly (b) Define a convex set. Show that C {x: € lR is convex, but not strictly convex. (5) (c) Find the characteristic polynomial of the following matrix : (5) (d) Find the dot product and cross product of the vectors d:llt'2j+6fr, and i = 1'2i+ cj-6k' (e) Show that the vectors (3,0,2), (7,0'9) and (4,1'2) form a basis for E3. (5) (f) Find the rank of the matrix A: 3-2 2. (a) Find the inverse of the following matrix : -l (b) For what values of )' and equations p. do the system of 2x+4y+2),2:2lt have (i) no solution, (ii) unique solution' and (iii) more than one solution. (a) Apply Gram-schmidt orthonormalization process to obtain an orthonormal basis for the subspace of P4 generated by the vectors ( 1,1,1,1,1), (b) If the system of equations (8) has a non-zero solution, then find the possible values of k. 4 for the (a) Verify the Cayley Hamilton Theorem matrix (b) Use gram Schmidt process to obtain orthonormal basis for R3(R) with standard inner product space, given vectors o, = (1,0,1), o, = (1,0,-l), and o, = (0,3,4). (8)