Addition of matrices

Addition of Matrices is an operation done on two or more matrics according to their corresponding entries. Matrix of same order can only be added. If there orders are different then addition operation cannot be applied on them.

Adding Matrices requires addition of corresponding elements of them. For example if two Matrices are added then elements in first row and first column of the two matrices will be added together to get the element in the first row and first column of the resultant matrix.

Two Matrices of order m × n (m is number of rows and n is number of columns) can be added:

Let sum of these = C = A+B then
C11 = a11 + b11, C12 = a12 + b12….,  C21 = a21 + b21, C22 = a22 + b22 and so on.

A + B = C =  ( )
Order of matrix C will also be m × n.
If two matrix are equal but opposite in sign, then there addition will be null matrix (whose all elements are zero). For example if A = ((1@2@5)) and B = ((-1@-2@-5)) then A+B = 0 as A+B = ((1+(-1)@2+(-2)@5+(-5)))= ((0@0@0))

Example 1) Add Matrices A and B if A = ((1&9@5&2))  and B = ((2&4@5&8))
Solution) Let sum of A and B be C. order of C will be same as that of A and B i.e. 2x2.
Elements of matrix C will be: C11, C 12, C 21, C22.
C11 = A11 + B11 = 1+2,
C12 = A12 + B12 = 9+4,
C21 = A21 + B21 = 5+5,
C22 = A22 + B22 = 2+8,
C = ((C11 = A11 + B11 &C12 = A12 + B12 @C21 = A21 + B21&C22 = A22 + B22))
C =   ((1 + 2&9 + 4@5 + 5 &2 + 8))
C = ((3&13@10&10))
Example 2) Perform addition of Matrices P and Q given as:
P =   ((2&0&- 3@5&3&7@3&- 7&1)), Q =  ((- 4&6&2@5&2&5@21&- 15&- 4))
Solution) let P+Q = R
R11 = P11 + Q11 = 2 +(-4) =-2,
R12 = P12 + Q12 = 0+6 = 6,
R13 = P13 + Q12 = -3+2 =-1
R21 = P21 + Q21 = 5+5 =10,
R22 = P22 + Q22 = 3+2 =5,
R23 = P23 + Q23 = 7+5 = 12
R31 = P31 + Q31 = 3+21=24
R32 = P32 + Q32 = -7+(-15) =-22
R33 = P33 + Q33 = 1+(-4)= -3
R = ((R_11&R_12&R_13@R_21&R_22&R_23@R_31&R_32&R_33 ))
R = ((-2&6&-1@10&5&12@24&-22&-3))