Solve Addition Matrices

A matrix is defined as the numbers are arranged in rows and columns. A matrix can be represents a capital letter. We have to locate the number in the form of rows and columns. In general row and column is denoted by the letter m and n respectively. An element can be represents ith row and jth column of the particular matrix and it is denoted by a_ij

            Example A= `[[1,-5],[2,-7]]` Where the element 2 is in a₂₁ [second row first column]

            In this article we shall discuss about the addition of matrix.

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Operation on Matrices:

• Addition of two matrices
• Subtraction of two matrices
• Multiplication of two matrices
• Division of two matrices

Addition of matrices:
Rules: If the two matrixes are same number of rows and columns. Then only the addition process can be done otherwise we can’t perform the addition in matrix
Thus, if A= [a_ij]_mxn    and  B = [b_ij] _mxn   then
   A+B = [a_ij  +b_ij] _{m xn}
Example problems on addition of two matrices:
A = `[[2,-4],[5,-7]]`   B = `[[3,6],[4,9]]`                  Solve the A+B
Solution:
            Both the rows and columns are equal. So we can perform the addition process.
A+B= `[[2+3,-4+6],[5+4,-7+9]]`
` =``[[5,2],[9,2]]`
`Hence the answer is ``[[5,2],[9,2]]`

Example problems on addition of two matrices:

A = `[[3,6,9],[12,2,3]]`   B = `[[5,7,-2],[-5,8,4]]`                  Solve the A+B
Solution:
            Both the rows and columns are equal. So we can perform the addition process.
A+B=`[[3+5,6+7,9-2],[12-5,2+8,3+4]]`
       =`[[8,13,7],[7,10,7]]`
Hence the solved answer is `[[8,13,7],[7,10,7]]`

Addition Theorem in matrix:

A matrix addition supports the commutative property. A+B = B+A for all similar matrices A and B
PROOF:
Let A =[a_ij]_mxn   and B = [b_ij]_mxn Then,
A+B= [a_ij]_mxn  +[b_ij]_mxn
        =[a_ij +b_ij]_mxn 
        =[b_ij+a_ij]_mxn 
        =[b_ij]_mxn +[a_ij]_mxn  =B+A
Hence the theorem proved A+B = B+A
Solve Problems on commutative property:
A=`[[4,5],[2,9]]`   B= `[[6,12],[11,15]]`
Solution:
Commutative property = A+B= B+A
First here we find A+B
A+B = `[[4+6,5+12],[2+11,9+15]]`
` = ``[[10,17],[13,24]]`
Then we have to find B+A
B+A =`[[6+4,12+5],[11+2,15+9]]`
` = ``[[10,17],[13,24]]`
`Hence A+B =B+A`


My forthcoming post is on Sum to Product and basic algebra test will give you more understanding about Algebra.

Practice Problem in Matrix Addition:

A= `[[2,4],[3,6]]``[[4,9],[5,8]]`
`Answer: ``[[6,13],[8,14]]`
`2.``[[11,13],[12,15]]``[[16,18],[17,13]]`
`Answer: ``[[27,31],[29,28]]`