This document provides tips for effectively studying math, specifically matrices. It recommends working hard, learning concepts rather than memorizing, building knowledge through teamwork and competition, and practicing regularly. Key matrix concepts covered include addition, subtraction, multiplication, determinants, expansions, minors, cofactors, and properties. The overall message is to start practicing, think of different approaches, and keep motivating yourself with honest feedback.
10. Rules....
Check for no. of columns is equal to no. of
rows.
Multiply each element of a row from each
element of column and ad it.
Repeat the process for each row.
12. Expansion of Determinants
+ - +
- + -
+ - + 3 3
Each element of first row and first
column is multiplied by that determinant
of order two which remain left after
hiding the row & column passing through
the elements.
13. Minor & Cofactors
x
a11 b12 c13
a21 b22 c23
a31 b32 c33
3 3
The determinant obtain by removing its i th
row and j th column is denoted by
M i j and is called minor of the element.
Cofactor = (-1)i+j.Mij
14. you will find a way
only wHen you Start
moving….
You will surprise to see that you got your
answer after moving few steps
15. Properties of Matrix
x Learn all the theorms
x Thumb rules
x Think a way and start solving the question,
“if it does not give you the answer, it will
give many other ways”
