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Addition of Two Matrices

We will learn how to find the addition of two matrices.

Two matrices A and B are conformable (compatible) for addition if A and B are of the same order.

The sum of A and B is a matrix of the same order and the elements of the matrix A + are obtained by adding the corresponding elements of A and B.

Example:

Let A = [12731], B = [9354], C = [795231].

(i) A + B can be found because A and B both are of the same order 2 × 2. Adding the corresponding elements,

A + B = [12+97+33+(5)(1)+4]

         = [211023]


(ii) A + C cannot be found because A and C are not of the same order. A is of the order 2 × 2 and C is of the order 2 × 3.


Solved Examples on Addition of Two Matrices

1. If A = [1573], B = [12109], find A + B.

Solution:

A + B can be found because A and B both are of the same order 2 × 2.

Now adding the corresponding elements we get,

A + B = [1573] + [12109]

          = [1+125+(1)7+03+9]

          = [134712]

Addition of Two Matrices


2. If X = [1001], Y = [0110], find sum of two matrices X and Y.

Solution:

X + Y can be found because X and Y both are of the same order 2 × 2.

Now adding the corresponding elements we get,

X + Y = [1001] + [0110]

          = [1+00+10+11+0]

          = [1111]





10th Grade Math

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