Algebra Matrices Online

Introduction to Learn Algebra Matrices online:

Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Matrix algebra is the part of the algebra that deals with the theory of matrices. Matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers. I like to share this free help with algebra 2 with you all through my article.



Learn Algebra Properties of Matrix Operations online:


Learn Algebra Properties of Matrix Operations online are as follows:

Learn Properties of Addition: Let a, b, and c be m*n matrices. We have

1. a + b = a + b

2. (a + b) + c = a + (b + c)

3. a + 0 = a

4. a + b = 0 if and only if b = -a

Learn Properties of Multiplication:

1. Let a, b, and c be three matrices. If products ab, (ab)c, bc, and a(bc), then we have

(ab)c = a (bc)

2. If a and ß are numbers, and a is a matrix, then we have

a(ßa) = (a ß)a

3. If a is a number, and a and b are two matrices that the product a·b is possible, then we have a(ab) = (aa)b = a(ab)

4. If A is an n*m matrix and 0 the m*k zero-matrix, then a0 = 0

Learn Properties of Addition and Multiplications:

1. Let a, b, and c be three matrices. If you can perform the appropriate products, then we have

(a+b)c = ab + bc

and

a(b+c) = ab + ac

2. If a and ß are numbers, a and b are matrices, then we have

a(a+b) = aa + a ß

and

(a + ß)a = aa + ßa

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Learning Example Problems for Algebra Matrices online:


Learning Example Problems for Algebra Matrices online are as follows:

Learn Example 1:

X=  `[[-1,0],[0,1]]` ,Y= `[[1,0],[0,-1]]` To evaluate XYand YX

Solution:



XY =  `[[-1,0],[1,0]]` ×`[[1,0],[0,-1]]`  = `[[-1,0],[0,1]]`



YZ = `[[-1,0],[0,1]]`


Example Problem 2:


Evaluate `[[1,2],[1,2]]`

Solution:

`[[1,2],[1,2]]`

[2-2]=0