BSc Mathematics SEM IV 2019 20 Oct 2019-20 ATKT MATHS LINEAR ALGEBRA Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q2 Figures to right Indicate full marks
2. Q3 Illustrations, in-depth answers and diagram will be appreciated
3. Q1 all (Smarks each) 15 marks
   • A) Multiple choice questions
   • i) Which of the following commands will create a list?
   • a) b) listl=[] c) d) All of these
   • ii) The dot product of (1,3,1) & (0,1,-1) is
   • d) None of these = iii) The dot product of (0,1,4) & (1,2,3) is
   • a) -10 b) 10 c)12 d) None of these
   • iv) A vector whose norm is called
   • a) Null b) basis c) Unit d) None of these
   • v) For any homogenous system solution
   • a) zero b) nonzero one d) None of these
   • B) Fill in the blanks
   • i) The output when we execute list (“Hello”) is
   • ii) If diagonal entry of squire matrix is one & non-diagonal entry is zero then matrix is
   • iii) To add a new element to a list we use command
   • iv) The absolute value of Hui is
   • v) Inverse of a matrix is
   • C) Answer the following question
4. Q1 Define dot product
5. Q2 Define dimension
6. Q3 Find dot product of (1.5), (4,-2)
7. Q4 Solve (1.1) + (0.1) + (0.1)
8. Q5 Determine the term characteric equation
9. Q2 Attempt the following (Any Three) 15 marks
   • a) Find the squire root of complex number 7-41
   • c) Write a python program to find conjugate of complex number
   • d) Are the following vectors are linearly dependant ?
   • e) Express in polar and exponential form
   • f) Check whether the set of all pairs-of real numbers of the form with operation + = (Ly + = (1, ky) is a vector space
10. Q3 Attempt the following (Any Three) 15 marks
    • a) Find the angle between the two vectors a = (2,3,4),b = (1, in IR?
    • b) Find null space in matrix
    • c) Let V be linear transformation then show that kerf = {0} iff f is injective
    • d) Consider subspace {(x, y, w,z)/x — y = O}and w, = wiy=z find basic & determination of i) ii)U2 i11)U,N V2
    • e) Check whether the set of functions are linearly independent 2 — x + +
    • f) If V, W are two subsets of a vector space V such that U is a subset of W then show that is a subset of where are annihilator of U,W respectively
11. Q4 Attempt the following (Any Three) 15 marks
    • a) Find orthonormal basis for subspace IR* whose generators are
    • b) Let a=(3,0),b=(2,1) find vector is span {a} that is closed to b is b' and distance
    • c) Find inner product, angle, orthogonality for p = +5 + 2x — x?
    • d) Write program in python to find g.c.d(240,36)
    • e) Let u,v be orthogonal vectors then prove that scaler || au + by Il
    • f) Explain internet worm
12. Q5 Attempt any three of following. 15 marks
    • a) Let be linear map be defined by =
    • b) Find eigen values & eigen vectors of [ 3 Let S be a subset of vector space V. prove that isa subspace of V
    • d) Express the following as linear combination of V3=(-1,-2,1)
    • e) Fill the table vector space basic dimension

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