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Add past question for mth203, wdu
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@udohjeremiah
udohjeremiah authored Dec 4, 2023
2 parents 9ba41c5 + e035b62 commit 09e4b9d
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267 changes: 267 additions & 0 deletions src/app/past-questions-archive/wdu/mth/2022_2023/200-level/1st-semester/mth203/page.jsx
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import Questions from "@/components/Questions";
import Answers from "@/components/Answers";

export default function MTH202() {
return (
<Questions
school="western delta university"
college="natural and applied sciences"
department="mathematics"
session="2022/2023"
semester="first semester"
courseCode="mth203"
courseTitle="linear algebra I"
allowedTime="2hrs: 30mins"
instruction="answer any THREE (3) questions"
>
<li>
<h4 className="mb-2 font-bold">Question 1</h4>
<ol className="flex list-[lower-alpha] flex-col gap-2">
<li>
What is a Vector Space?{" "}
<strong className="whitespace-nowrap">(8 marks)</strong>
<Answers questionNumber="1a" />
</li>
<li>
Give three (3) examples of a vector space{" "}
<strong className="whitespace-nowrap">(6 marks)</strong>
<Answers questionNumber="1b" />
</li>
<li>
Define the following and give one (1) example in each case:
<ol className="mx-4 list-[lower-roman]">
<li>Echelon matrix</li>
<li>Orthogonal matrix</li>
<li>Skew-symmetric matrix</li>
</ol>
<strong className="whitespace-nowrap">(9 marks)</strong>
<Answers questionNumber="1c" />
</li>
</ol>
</li>

<li>
<h4 className="mb-2 font-bold">Question 2</h4>
<ol className="flex list-[lower-alpha] flex-col gap-2">
<li>
Reduce the matrix below to echelon form: <br />A ={" "}
<div className="inline-flex">
<span className="text-7xl">[</span>{" "}
<div className="flex flex-col">
<div className="flex gap-6">
<span> -4 </span>
<span>1</span>
<span> -6 </span>
</div>
<div className="flex gap-6">
<span>1</span>
<span>2</span>
<span> -5 </span>
</div>
<div className="flex gap-6">
<span>6</span>
<span>3</span>
<span>4</span>
</div>
</div>
<span className="text-7xl">]</span>
</div>{" "}
<strong className="whitespace-nowrap">(10 marks)</strong>
<Answers questionNumber="2a" />
</li>
<li>
Let A ={" "}
<div className="inline-flex">
<span className="text-5xl">(</span>{" "}
<div className="flex flex-col">
<div className="flex gap-6">
<span>7</span>
<span>3</span>
</div>
<div className="flex gap-6">
<span>3</span>
<span> -1 </span>
</div>
</div>
<span className="text-5xl">)</span>
</div>
, find an orthogonal matrix P such that D = P<sup>-1</sup>AP is
diagonal <strong className="whitespace-nowrap">(13 marks)</strong>
<Answers questionNumber="2b" />
</li>
</ol>
</li>

<li>
<h4 className="mb-2 font-bold">Question 3</h4>
<ol className="flex list-[lower-alpha] flex-col gap-2">
<li>
Given A ={" "}
<div className="inline-flex">
<span className="text-7xl">[</span>{" "}
<div className="flex flex-col">
<div className="flex gap-6">
<span>1</span>
<span> -1 </span>
<span>1</span>
</div>
<div className="flex gap-6">
<span>2</span>
<span>4</span>
<span>3</span>
</div>
<div className="flex gap-6">
<span>5</span>
<span>6</span>
<span> -2 </span>
</div>
</div>
<span className="text-7xl">]</span>
</div>
, using elementary row operations, reduce A to row echelon form{" "}
<strong className="whitespace-nowrap">(10 marks)</strong>
<Answers questionNumber="3a" />
</li>
<li>
Given A ={" "}
<div className="inline-flex">
<span className="text-7xl">[</span>{" "}
<div className="flex flex-col">
<div className="flex gap-6">
<span>1</span>
<span>0</span>
<span>2</span>
</div>
<div className="flex gap-6">
<span>2</span>
<span> -1 </span>
<span>3</span>
</div>
<div className="flex gap-6">
<span>4</span>
<span>1</span>
<span>8</span>
</div>
</div>
<span className="text-7xl">]</span>
</div>
, find A<sup>-1</sup> using elementary row operations{" "}
<strong className="whitespace-nowrap">(13 marks)</strong>
<Answers questionNumber="3b" />
</li>
</ol>
</li>

<li>
<h4 className="mb-2 font-bold">Question 4</h4>
<ol className="flex list-[lower-alpha] flex-col gap-2">
<li>
Solve the system, using Gaussian elimination method:
<ol className="mx-4 list-[lower-roman]">
<li>x + 2y + z = 3</li>
<li>2x + 5y - z = -4</li>
<li>3x + 2y - z = 5</li>
</ol>{" "}
<strong className="whitespace-nowrap">(13 marks)</strong>
<Answers questionNumber="4a" />
</li>
<li>
Given Y ={" "}
<div className="inline-flex">
<span className="text-5xl">[</span>{" "}
<div className="flex flex-col">
<div className="flex gap-6">
<span>
Y<sub>1</sub>
</span>
</div>
<div className="flex gap-6">
<span>
Y<sub>2</sub>
</span>
</div>
</div>
<span className="text-5xl">]</span>
</div>
and A ={" "}
<div className="inline-flex">
<span className="text-5xl">[</span>{" "}
<div className="flex flex-col">
<div className="flex gap-6">
<span>2</span>
<span>2</span>
</div>
<div className="flex gap-6">
<span>2</span>
<span>0</span>
</div>
</div>
<span className="text-5xl">]</span>
</div>
, find Y<sup>1</sup>AY{" "}
<strong className="whitespace-nowrap">(10 marks)</strong>
<Answers questionNumber="4b" />
</li>
</ol>
</li>

<li>
<h4 className="mb-2 font-bold">Question 5</h4>
If A ={" "}
<div className="inline-flex">
<span className="text-5xl">(</span>{" "}
<div className="flex flex-col">
<div className="flex gap-6">
<span>2</span>
<span>2</span>
</div>
<div className="flex gap-6">
<span>1</span>
<span>3</span>
</div>
</div>
<span className="text-5xl">)</span>
</div>
<ol className="mx-4 list-[lower-roman]">
<li>
Find all eigen values and corresponding eigenvectors.{" "}
<strong className="whitespace-nowrap">(5 marks)</strong>
<Answers questionNumber="5i" />
</li>
<li>
Find a non singular matrix P such that D = P<sup>-1</sup>AP is
diagonal and P<sup>-1</sup>{" "}
<strong className="whitespace-nowrap">(10 marks)</strong>
<Answers questionNumber="5ii" />
</li>
<li>
Find A<sup>6</sup> and F(A), where t<sup>3</sup> - 3t<sup>2</sup> +
7t + 3 <strong className="whitespace-nowrap">(8 marks)</strong>
<Answers questionNumber="5iii" />
</li>
</ol>
</li>

<li>
<h4 className="mb-2 font-bold">Question 1</h4>
<ol className="flex list-[lower-alpha] flex-col gap-2">
<li>
When are vectors linearly dependent?{" "}
<strong className="whitespace-nowrap">(3 marks)</strong>
<Answers questionNumber="6a" />
</li>
<li>
Determine whether or not U and V are linearly dependent.
<ol className="mx-4 list-[lower-roman]">
<li>U = (1, -3), V = (-2, 6)</li>
<li>U = (1, 2, -3), V = (4, 5, -6)</li>
<li>U = (2, 4, -8), V = (3, 6, -2)</li>
</ol>
<strong className="whitespace-nowrap">(15 marks)</strong>
<Answers questionNumber="6b" />
</li>
</ol>
</li>
</Questions>
);
}
8 changes: 4 additions & 4 deletions src/app/past-questions-archive/wdu/mth/2022_2023/200-level/1st-semester/page.jsx
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Expand Up @@ -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",
},
],
};

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