EXAMSHARE

Western Delta University, Oghara Delta State

department of mathematics
college of natural and applied sciences
western delta university

second semester examination 2022/2023 session

mth202 - linear algebra II time: 2hrs: 30mins

answer any other THREE (3) questions only

  1. Question 1

    1. Decompose A =
      (
      251
      31-2
      4102
      )
      into symmetric and skew symmetric matrices (15 marks)
    2. If A =
      (
      10-12
      346-1
      25-97
      )
      . Find:
      1. row space of A
      2. column space of A
      (8 marks)

  2. Question 2

    1. Diagonalize the matrix A =
      (
      12
      30
      )
      (23 marks)

  3. Question 3

    1. State the dimension theorem (7 marks)
    2. State the standard basis for R4 (4 marks)
    3. Reduce these matrices to Gauss Jordan form:
      1. (
        22-1
        003
        1-12
        )
      2. (
        110
        121
        -112
        )
      (12 marks)

  4. Question 4

    1. If A =
      (
      123
      10-1
      231
      )
      . Find A-1, using elementary row operation (23 marks)

  5. Question 5

    1. Let R be a non-empty set with two binary operations of addition and multiplication, then define the following with examples:
      1. A ring
      2. Subring S or R
      3. Integral domain
      (15 marks)
    2. If D is an integral domain, for some a, b, c, p, define the following with examples:
      1. b divides a in D
      2. associate of a ∈ D
      3. P ∈ D in irreducible
      4. Unique factorization
      (8 marks)

  6. Question 6

    1. Define the following with example:
      1. Orthogonal basis
      2. Orthonormal basis
      (15 marks)
    2. What are the following:
      1. subspace of V of Rn
      2. null space of A
      3. row space of A
      4. column space of A
      (8 marks)