Learn Matrices Online

Introduction about learn matrices online:

Matrix  is a rectangular array of numbers, arranged in rows and columns.

The number of rows (say m) and the number of columns (say n) find the order of the matrix.

It can be written as m x n (to be read as m by n).

Learn matrices online:

The plural  of matrix is matrices. Matrix is usually denoted by capital letters such as A, B, C,…

The Matrices can be defined as the set of m × n numbers arranged in a rectangular form. here m is row of the matrix and  n is column of the matrix.

for eg: A =  `[[a,b],[c,d]]` is a matrix of order 2 × 2.

Matrices Online is  used to verify the consistency of the linear equation system. Also, used to find the solution for the linear equation system with two and three variables by matrix inversion. Please express your views of this topic Matrices Calculator by commenting on blog.



Example Problems to learn solving online matrices:


Learn online solving  matrices Example 1:

If  `[[2,x],[x,1]]` = `[[5,2],[4,1]]`   ,then find x?

Solution:

Since the given matrices are equal,their corresponding elements must be equal.

Equating the corresponding elements, implies

2 - x2 = 5 - 8

x2 = 5 then

x = `+- sqrt(5)` .

Learn solving online matrices Example 2:

Evaluate determinant   = `[[1,2,2],[2,2,1],[1,2,1]]`

Solution:

= 1(2-2) - 2(2-1) + 2(4-2)

= 0 - 2(1) + 2(2)

= -2 + 4

= 2.

Learn solving online matrices Example 3:

If  `[[x+3,z+4,2y-7],[-6,a-1,0],[b-3,-21,0]]` = `[[0,6,3y-2],[-6,-3,2c+2],[2b+4,-21,0]]`   Find the values of a, b, c, x, y and z.

Solution:

Since the given matrices are equal,their corresponding elements must be equal.

Equating the corresponding elements, implies

x + 3 = 0,

z + 4 = 6,

2y – 7 = 3y – 2,

a – 1 = – 3,

0 = 2c + 2,

b – 3 = 2b + 4,

By Simplification,

Answers:

a = – 2,

b = – 7,

c = – 1,

x = – 3,

y = –5,

z = 2.

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Learn online solving Matrices Example 4:


Find the values of a, b, c, and d from the following matrix equation:

`[[2a+b,a-2d],[5c-d,4c+3d]]` =` [[4,-3],[11,24]]` .

Solution:

since the given matrices are equal,their corresponding elements must be equal.

equating the corresponding elements, implies

2a + b = 4,

5c – d = 11,

a – 2b = – 3,

4c + 3d = 24,

By Simplification,

Answers:

a = 1,

b = 2,

c = 3 and

d = 4.

Learn online Solving matrices Example 5:

If A = `[[sqrt(3) ,1,-1],[2,3,0]]` and B = `[[2,sqrt(5),1],[-2,3,1/2]]` , find A + B.

Solution:

Since, the two matrices is of the same order.

Matrix addition is possible, implies

A+B = `[[sqrt(3)+2,1+sqrt(5),-1+1],[2-2,3+3,0+1/2]]`

= `[[2+sqrt(3),1+sqrt(5),0],[0,6,1/2]]` .