From e035b6237db32cd233bbd2c6853f6548c76740e8 Mon Sep 17 00:00:00 2001 From: Udoh Jeremiah Date: Mon, 4 Dec 2023 19:11:45 +0100 Subject: [PATCH] Add past question for mth203, wdu --- .../200-level/1st-semester/mth203/page.jsx | 267 ++++++++++++++++++ .../2022_2023/200-level/1st-semester/page.jsx | 8 +- 2 files changed, 271 insertions(+), 4 deletions(-) create mode 100644 src/app/past-questions-archive/wdu/mth/2022_2023/200-level/1st-semester/mth203/page.jsx diff --git a/src/app/past-questions-archive/wdu/mth/2022_2023/200-level/1st-semester/mth203/page.jsx b/src/app/past-questions-archive/wdu/mth/2022_2023/200-level/1st-semester/mth203/page.jsx new file mode 100644 index 0000000..73ba4f1 --- /dev/null +++ b/src/app/past-questions-archive/wdu/mth/2022_2023/200-level/1st-semester/mth203/page.jsx @@ -0,0 +1,267 @@ +import Questions from "@/components/Questions"; +import Answers from "@/components/Answers"; + +export default function MTH202() { + return ( + +
  • +

    Question 1

    +
      +
    1. + What is a Vector Space?{" "} + (8 marks) + +
      2. +
    2. + Give three (3) examples of a vector space{" "} + (6 marks) + +
      3. +
    3. + Define the following and give one (1) example in each case: +
        +
      1. Echelon matrix
        2. +
      2. Orthogonal matrix
        3. +
      3. Skew-symmetric matrix
        4. +
      + (9 marks) + +
      4. +
    +
    • + +
  • +

    Question 2

    +
      +
    1. + Reduce the matrix below to echelon form:
      A ={" "} +
      + [{" "} +
      +
      + -4 + 1 + -6 +
      +
      + 1 + 2 + -5 +
      +
      + 6 + 3 + 4 +
      +
      + ] +
      {" "} + (10 marks) + +
      2. +
    2. + Let A ={" "} +
      + ({" "} +
      +
      + 7 + 3 +
      +
      + 3 + -1 +
      +
      + ) +
      + , find an orthogonal matrix P such that D = P-1AP is + diagonal (13 marks) + +
      3. +
    +
    • + +
  • +

    Question 3

    +
      +
    1. + Given A ={" "} +
      + [{" "} +
      +
      + 1 + -1 + 1 +
      +
      + 2 + 4 + 3 +
      +
      + 5 + 6 + -2 +
      +
      + ] +
      + , using elementary row operations, reduce A to row echelon form{" "} + (10 marks) + +
      2. +
    2. + Given A ={" "} +
      + [{" "} +
      +
      + 1 + 0 + 2 +
      +
      + 2 + -1 + 3 +
      +
      + 4 + 1 + 8 +
      +
      + ] +
      + , find A-1 using elementary row operations{" "} + (13 marks) + +
      3. +
    +
    • + +
  • +

    Question 4

    +
      +
    1. + Solve the system, using Gaussian elimination method: +
        +
      1. x + 2y + z = 3
        2. +
      2. 2x + 5y - z = -4
        3. +
      3. 3x + 2y - z = 5
        4. +
      {" "} + (13 marks) + +
      2. +
    2. + Given Y ={" "} +
      + [{" "} +
      +
      + + Y1 + +
      +
      + + Y2 + +
      +
      + ] +
      + and A ={" "} +
      + [{" "} +
      +
      + 2 + 2 +
      +
      + 2 + 0 +
      +
      + ] +
      + , find Y1AY{" "} + (10 marks) + +
      3. +
    +
    • + +
  • +

    Question 5

    + If A ={" "} +
    + ({" "} +
    +
    + 2 + 2 +
    +
    + 1 + 3 +
    +
    + ) +
    +
      +
    1. + Find all eigen values and corresponding eigenvectors.{" "} + (5 marks) + +
      2. +
    2. + Find a non singular matrix P such that D = P-1AP is + diagonal and P-1{" "} + (10 marks) + +
      3. +
    3. + Find A6 and F(A), where t3 - 3t2 + + 7t + 3 (8 marks) + +
      4. +
    +
    • + +
  • +

    Question 1

    +
      +
    1. + When are vectors linearly dependent?{" "} + (3 marks) + +
      2. +
    2. + Determine whether or not U and V are linearly dependent. +
        +
      1. U = (1, -3), V = (-2, 6)
        2. +
      2. U = (1, 2, -3), V = (4, 5, -6)
        3. +
      3. U = (2, 4, -8), V = (3, 6, -2)
        4. +
      + (15 marks) + +
      3. +
    +
    • +     + ); +} diff --git a/src/app/past-questions-archive/wdu/mth/2022_2023/200-level/1st-semester/page.jsx b/src/app/past-questions-archive/wdu/mth/2022_2023/200-level/1st-semester/page.jsx index 5ff2c7c..9ae6573 100644 --- a/src/app/past-questions-archive/wdu/mth/2022_2023/200-level/1st-semester/page.jsx +++ b/src/app/past-questions-archive/wdu/mth/2022_2023/200-level/1st-semester/page.jsx @@ -2,14 +2,14 @@ import LinkList from "@/components/LinkList"; const courses = { "": [ - { - name: "MTH 211 - Statistics", - route: "1st-semester/mth211", - }, { name: "MTH 203 - Linear Algebra I", route: "1st-semester/mth203", }, + { + name: "MTH 211 - Statistics", + route: "1st-semester/mth211", + }, ], };