Linear Algebra

Pre-requisite MAT2002 Applications of Differential and Difference Equations Syllabus Version 1.1 Course Objectives 1. Understanding basic concepts of linear algebra to illustrate its power and utility through applications to computer science and Engineering. 2. Apply the concepts of vector spaces, linear transformations, matrices and inner product spaces in engineering. 3. Solve problems in cryptography, computer graphics and wavelet transforms Course Outcomes At the end of this cours...

Table of Contents Preface vii 1 Preliminaries 1 1.1 Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.2 Answers for Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Set Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . ...

1 Matrices, Vectors and Their Operations 1 1.1 Basic definitions and notations 2 1.2 Matrix addition and scalar-matrix multiplication 5 1.3 Matrix multiplication 7 1.4 Partitioned matrices 14 1.4.1 2  2 partitioned matrices 14 1.4.2 General partitioned matrices 16 1.5 The “trace” of a square matrix 18 1.6 Some special matrices 20 1.6.1 Permutation matrices 20 1.6.2 Triangular matrices 22 1.6.3 Hessenberg matrices 24 1.6.4 Sparse matrices 26 1.6.5 Banded matrices 27 1.7 Exercis...

Linear Algebra Guide

Linear Algebra

UESTION TWO (20 MARKS) a) Let T: → be defined by , = (x+y, y). Show that T is a linear transformation. Find f(A) when A QUESTION THREE (20 MARKS) a) If A and B are similar matrices show that they have the same determinant. (5 Marks) 2 1 0 0 0 2 0 0 (6 Marks) 0 0 1 1 0 0 − b) Find the characteristics polynomial of the matrix A 2 4

University Examinations 2023/2024 LINEAR ALGEBRA I QUESTION ONE – (30 MAKS) a) Solve for the constants a, b and c if a 5i ~ + ~j b ~j+ k~ ck~ =8~i+3~j− k~ (4 marks) b) Given that u = i+ 2 j+ k and v = j+ 3k , determine the cross product of u and v. ~ ~ ~ ~ ~ ~ ~ ~ ~ (3 marks) c) Write the polynomial = +4 − 3 as a linear combination of...

Stepwise solution of Ex 2.8 from Calculus (Anton,Bivens,Davis)with diagram to explain the geometrical properties of the issue concerned.

Calculus 10 TH edition Ex 2.8 . Complete stepwise solutions from Question No 1 to Question No 47 with diagram to explain the geometrical properties. The main topic is: DIFFERENTIATING EQUATIONS TO RELATE RATES

Linear algebra is the branch of mathematics concerning linear equations such as: {displaystyle a_{1}x_{1}+cdots +a_{n}x_{n}=b, } linear maps such as: {displaystyle mapsto a_{1}x_{1}+cdots +a_{n}x_{n}, } and their representations in vector spaces and through matrices.