This document is a tutorial by Dr. Mehar Chand on the properties associated with spheres and basic matrix mathematics. It includes various examples and exercises related to matrices, such as determining orders and specific elements of given matrices. The content aims to educate students on fundamental concepts in mathematics with video resources provided for further learning.

1. Properties
Associated
with Sphere
Dr. Mehar
Chand
Examples
Video
Tutorial-II: Matrices
Basic Mathematics:
Matrices
Dr. Mehar Chand
Department of Mathematics
Baba Farid College, Bathinda-151001
April 21, 2020
Dr. Mehar Chand Properties Associated with Sphere

2. Properties
Associated
with Sphere
Dr. Mehar
Chand
Examples
Video
Contents
1 Examples
2 Full video Lecture
Dr. Mehar Chand Properties Associated with Sphere

3. Properties
Associated
with Sphere
Dr. Mehar
Chand
Examples
Video
Examples
Ex-1 Let
A = [aij ] =


2 −1 5 7
0 8 1 −3
15 2 7
3 9


Find the order of A. Also find the elements a24, a23, a14
Dr. Mehar Chand Properties Associated with Sphere

4. Properties
Associated
with Sphere
Dr. Mehar
Chand
Examples
Video
Examples
Ex-2 If a matrix has 24 elements, what are the possible
orders it can have? What, if it has 13 elements.
Ex-3 Construct a 3 × 2 matrix whose elements are given by
aij = 1
2 |i − 3j|
Ex-4 If
A =
cos α − sin α
sin α cos α
then for what value of α is A an identity matrix?
Ex-5 Find the value of x and y, if
x + 2y 3y
4x 2
=
0 −3
8 2
Dr. Mehar Chand Properties Associated with Sphere

5. Properties
Associated
with Sphere
Dr. Mehar
Chand
Examples
Video
Full video Lecture
To see full video lecture visit the below link
https://youtu.be/hEId2ZuD4Qc
Dr. Mehar Chand Properties Associated with Sphere

6. Properties
Associated
with Sphere
Dr. Mehar
Chand
Examples
Video
Thank you
Dr. Mehar Chand Properties Associated with Sphere