Question

what is a matrix, and it's applications and it's uses
what is the main function of matrix and it's types

plzz urgent answer

Answer 1

matrix :- A rectangular array of mn number in the form of m horizontal lines (called rows ) and n vertical lines ( called columns ) , is called a matrix of order m by n . see the figure for example .
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Type of matrix :- there are many types of matrix but some are important which I want to give here :

1. row matrix
2. column matrix
3. zero matrix or null matirx
4. vertical matrix
5. square matrix
6. horizontal matrix
7.Diagonal matrix
8.scalar matrix
9. unit matrix
10. uppar traingular matrix
11.lower triangular matrix
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application of matrix :
Matrix and it's close relative ' determinant' are very important tools for solving linear Algebra .

Consider a system of linear equations
a₁₁x₁ + a₁₂x₂+....+a₁ⅈxⅈ = b₁
a₂₁x₁+a₂₂x₂+....+a₂ⅈxⅈ = b₂
..... ..... ... .. ...... ....
..... ....... ........... ........
aⅈ₁x₁+aⅈ₂x₂+....+aⅈⅈxⅉ =bⅈ

we can express this in single matrix equation
A.X = B
where A is matrix of coefficient of variables and X is matrix of variable and
B is a matrix of constant .

Let | A | ≠ 0 so, that A-¹ exist uniquely
pre -multiplying both sides of AX = B by A-¹ , we get
X = A-¹B
hence, X = A-¹B is the unique splution of
AX = B when | A | ≠ 0