Skip to content

Commit

Permalink
Merge pull request #28 from udohjeremiah/dev
Browse files Browse the repository at this point in the history 
Adds past question for mth202-linear algebra II, wdu
  • Loading branch information
@udohjeremiah
udohjeremiah authored Dec 3, 2023
2 parents a16bfd3 + f81d682 commit 8d17078
Show file tree
Hide file tree
Showing 3 changed files with 287 additions and 1 deletion.
269 changes: 269 additions & 0 deletions src/app/past-questions-archive/wdu/mth/2022_2023/200-level/2nd-semester/mth202/page.jsx
View file
Original file line number Diff line number Diff line change
@@ -0,0 +1,269 @@
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="second semester"
courseCode="mth202"
courseTitle="linear algebra II"
allowedTime="2hr: 30mins"
instruction="answer any other THREE (3) questions only"
>
<li>
<h4 className="mb-2 font-bold">Question 1</h4>
<ol className="flex list-[lower-alpha] flex-col gap-2">
<li>
Decompose A ={" "}
<div className="inline-flex">
<span className="text-7xl">(</span>{" "}
<div className="flex flex-col">
<div className="flex gap-6">
<span>2</span>
<span>5</span>
<span>1</span>
</div>
<div className="flex gap-6">
<span>3</span>
<span>1</span>
<span>-2</span>
</div>
<div className="flex gap-6">
<span>4</span>
<span>10</span>
<span>2</span>
</div>
</div>
<span className="text-7xl">)</span>
</div>{" "}
into symmetric and skew symmetric matrices{" "}
<strong className="whitespace-nowrap">(15 marks)</strong>
<Answers questionNumber="1a" />
</li>
<li>
If 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>-1</span>
<span>2</span>
</div>
<div className="flex gap-6">
<span>3</span>
<span>4</span>
<span>6</span>
<span>-1</span>
</div>
<div className="flex gap-6">
<span>2</span>
<span>5</span>
<span>-9</span>
<span>7</span>
</div>
</div>
<span className="text-7xl">)</span>
</div>
. Find:
<ol className="mx-4 list-[lower-roman]">
<li>row space of A</li>
<li>column space of A</li>
</ol>
<strong className="whitespace-nowrap">(8 marks)</strong>
<Answers questionNumber="1b" />
</li>
</ol>
</li>

<li>
<h4 className="mb-2 font-bold">Question 2</h4>
<ol className="flex list-[lower-alpha] flex-col gap-2">
<li>
Diagonalize the matrix A ={" "}
<div className="inline-flex">
<span className="text-5xl">(</span>{" "}
<div className="flex flex-col">
<div className="flex gap-6">
<span>1</span>
<span>2</span>
</div>
<div className="flex gap-6">
<span>3</span>
<span>0</span>
</div>
</div>
<span className="text-5xl">)</span>
</div>
<strong className="whitespace-nowrap">(23 marks)</strong>
<Answers questionNumber="2a" />
</li>
</ol>
</li>

<li>
<h4 className="mb-2 font-bold">Question 3</h4>
<ol className="flex list-[lower-alpha] flex-col gap-2">
<li>
State the dimension theorem{" "}
<strong className="whitespace-nowrap">(7 marks)</strong>
<Answers questionNumber="3a" />
</li>
<li>
State the standard basis for R<sup>4</sup>{" "}
<strong className="whitespace-nowrap">(4 marks)</strong>
<Answers questionNumber="3b" />
</li>
<li>
Reduce these matrices to Gauss Jordan form:
<ol className="mx-4 list-[lower-roman]">
<li>
<div className="inline-flex">
<span className="text-7xl">(</span>{" "}
<div className="flex flex-col">
<div className="flex gap-6">
<span>2</span>
<span>2</span>
<span>-1</span>
</div>
<div className="flex gap-6">
<span>0</span>
<span>0</span>
<span>3</span>
</div>
<div className="flex gap-6">
<span>1</span>
<span>-1</span>
<span>2</span>
</div>
</div>
<span className="text-7xl">)</span>
</div>
</li>
<li>
<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>0</span>
</div>
<div className="flex gap-6">
<span>1</span>
<span>2</span>
<span>1</span>
</div>
<div className="flex gap-6">
<span>-1</span>
<span>1</span>
<span>2</span>
</div>
</div>
<span className="text-7xl">)</span>
</div>
</li>
</ol>
<strong className="whitespace-nowrap">(12 marks)</strong>
<Answers questionNumber="3c" />
</li>
</ol>
</li>

<li>
<h4 className="mb-2 font-bold">Question 4</h4>
<ol className="flex list-[lower-alpha] flex-col gap-2">
<li className="list-none">
If A ={" "}
<div className="inline-flex">
<span className="text-7xl">(</span>{" "}
<div className="flex flex-col">
<div className="flex gap-6">
<span>1</span>
<span>2</span>
<span>3</span>
</div>
<div className="flex gap-6">
<span>1</span>
<span>0</span>
<span>-1</span>
</div>
<div className="flex gap-6">
<span>2</span>
<span>3</span>
<span>1</span>
</div>
</div>
<span className="text-7xl">)</span>
</div>
. Find A<sup>-1</sup>, using elementary row operation{" "}
<strong className="whitespace-nowrap">(23 marks)</strong>
<Answers questionNumber="4" />
</li>
</ol>
</li>

<li>
<h4 className="mb-2 font-bold">Question 5</h4>
<ol className="flex list-[lower-alpha] flex-col gap-2">
<li>
Let R be a non-empty set with two binary operations of addition and
multiplication, then define the following with examples:
<ol className="mx-4 list-[lower-roman]">
<li>A ring</li>
<li>Subring S or R</li>
<li>Integral domain</li>
</ol>
<strong className="whitespace-nowrap">(15 marks)</strong>
<Answers questionNumber="5a" />
</li>
<li>
If D is an integral domain, for some a, b, c, p, define the
following with examples:
<ol className="mx-4 list-[lower-roman]">
<li>b divides a in D</li>
<li>associate of a ∈ D</li>
<li>P ∈ D in irreducible</li>
<li>Unique factorization</li>
</ol>
<strong className="whitespace-nowrap">(8 marks)</strong>
<Answers questionNumber="5b" />
</li>
</ol>
</li>

<li>
<h4 className="mb-2 font-bold">Question 6</h4>
<ol className="flex list-[lower-alpha] flex-col gap-2">
<li>
Define the following with example:
<ol className="mx-4 list-[lower-roman]">
<li>Orthogonal basis</li>
<li>Orthonormal basis</li>
</ol>
<strong className="whitespace-nowrap">(15 marks)</strong>
<Answers questionNumber="6a" />
</li>
<li>
What are the following:
<ol className="mx-4 list-[lower-roman]">
<li>
subspace of V of R<sup>n</sup>
</li>
<li>null space of A</li>
<li>row space of A</li>
<li>column space of A</li>
</ol>
<strong className="whitespace-nowrap">(8 marks)</strong>
<Answers questionNumber="6b" />
</li>
</ol>
</li>
</Questions>
);
}
14 changes: 14 additions & 0 deletions src/app/past-questions-archive/wdu/mth/2022_2023/200-level/2nd-semester/page.jsx
View file
Original file line number Diff line number Diff line change
@@ -0,0 +1,14 @@
import LinkList from "@/components/LinkList";

const courses = {
"": [
{
name: "MTH 202 - Linear Algebra II",
route: "2nd-semester/mth202",
},
],
};

export default function _2nd_semester() {
return <LinkList items={courses} isOrdered={true} />;
}
5 changes: 4 additions & 1 deletion src/app/past-questions-archive/wdu/mth/2022_2023/200-level/page.jsx
View file
Original file line number Diff line number Diff line change
@@ -1,7 +1,10 @@
import LinkList from "@/components/LinkList";

const semesters = {
"": [{ name: "1st Semester", route: "200-level/1st-semester" }],
"": [
{ name: "1st Semester", route: "200-level/1st-semester" },
{ name: "2nd Semester", route: "200-level/2nd-semester" },
],
};

export default function _200_level() {
Expand Down

0 comments on commit 8d17078

Please sign in to comment.