Adding Two Matrices

We know that the arrangements of numbers in rows and columns is called a matrix. Suppose a matrix has a m rows and n columns, Then its order can be written as m` xx` n. This can be read as m by n.  Two matrices of same order can be added or can be subtracted.  IF the orders are different, we say that the addition or subtraction of matrices is not defined.  Now let us learn how to add two matrices.

Having problem with Adding Rational Numbers keep reading my upcoming posts, i will try to help you.

Let A = `([a, b], [c, d]) ` and B = `([c, f], [g, h])`Since orders of A and B are of 2 `xx ` 2 and same, A + B is defined. that means we can add the matrices A and B as per the definition.

Therefore A + B = `([a, b], [c, d])` + `([e, f], [g, h])`

= `([a+e ,b +f], [c+g, d+h])`

Here add the first two values, second two values, third two values and fourth two values. Generally during the addition two matrices, the corresponding values are added.  Here the resultant matrix A+B will also be of same order.

Example problems on adding of two matrices.

Ex 1: Given: A = `([3, 4], [6, 7])` , B = `([2, 5], [8, 9])` find A + B.

Solution: A + B = `([3, 4], [6, 7]) + ([2, 5], [8, 9])`

= `([3+2, 4+5], [6+8, 7+9])` = `([5, 9], [14, 16])`

Therefore A+B = `([5, 9], [14, 16])`

Ex 2: Given: A – B = `([5, 3], [4, 2])` where A = `([1, b], [c, d])` and B = `([1, 3], [2,-2])`

Find the value of a, b, c and d.

Solution: Given: A – B = `([5, 3], [4, 2])`

Therefore A = `([5, 3], [4, 2])` + B = `([5, 3], [4, 2])` + `([1, 3], [2,-2])`

= `([5+1, 3+3], [4+2, 2-2])` = `([6, 6], [6, 0])`

Therefore A = `([a, b], [c, d])` = `([6, 6], [6, 0])`

If two matrices of same order are equal, then the corresponding values are equal.

Therefore, a = 6, b = 6, c = 6 and d = 0.

Ex 3: Given: X + A  = `([1,6],[8,9]) ` and A = `([3,-2],[-1,4])` Find x.

Solution: Given: X + A = `([1, 6], [8, 9])`

Therefore X = `([1, 6], [8, 9])` – A =  `([1, 6], [8, 9])` – `([3,-2], [-1, 4])`

= `([1, 6], [8, 9])` + `([-3,2],[1,-4])`   (Here multiply the minus sign through out the elments of A)

Therefore X = `([1 -3, 6 +2], [8+1, 9 -4])` = `([-2, 8], [9, 5])` .

My forthcoming post is on Define Stem and Leaf Plot and Decimal Place values will give you more understanding about Algebra.

Practice problems on adding of two problems:

(1) Find the sum of the following matrices: A = `([4, 7], [8, 9])` and B = `([6, 4], [3, 2])`

[Ans: A + B = `([10, 11], [11, 11])`

2) Find the matrix A in the given equation A – B = `([7, 4], [3, 2])` ,

where B = `([1, 3], [2, 4])`

[Ans: A = `([8, 7], [5, 6])`