# HOW TO ADD TWO MATRICES

How to Add Two Matrices ?

Here we are going to see how to add two or more matrices.

Two matrices can be added or subtracted if they have the same order. To add or subtract two matrices, simply add or subtract the corresponding elements.

## How to Add Two Matrices - Examples

Question 1 :

If A =

then verify that

(i) A + B = B + A (ii) A + (−A) = (−A) + A = O.

Solution :

(i) A + B =

B + A  =

Hence proved.

(ii) A + (−A)

(−A) + A =

A + (-A)  = (−A) + A = O.

Hence proved.

Question 2 :

If

then verify that A + (B + C) = (A + B) + C.

Solution :

L.H.S

B + C  =

R.H.S

A + B  =

Hence it is proved.

Question 3 :

Find X and Y if

Solution :

By applying the value of x in (1), we get

Question 4 :

find the value of (i) B - 5A (ii) 3A - 9B

(i) B - 5A

(ii) 3A - 9B

Question 5 :

Find the values of x, y, z if

Solution :

x - 3  =  0 ----(1)    3x - z  =  0 -----(2)

x  =  3

By applying the value of x in (2), we get

3(3) - z  =  0

-z  =  -9

z  =  6

x + y + 7  =  1 ----(3)

3 + y + 7  =  1

y  =  1 - 10

y  =  -9

(ii)  By combining the row matrices and equating the corresponding terms, we get

x + y  =  4  ---(1)

y - z + 4  =  8  ----(2)

z + 3 + 3  =  16----(3)

z + 6  =  16

z  =  16 - 6  =  10

By applying the value of z in (2), we get

y - 10 + 4  =  8

y - 6  =  8

y  =  8 + 6

y  =  14

By applying the value of y in (1), we get

x + 14  =  4

x  =  4 - 14

x  =  -10

After having gone through the stuff given above, we hope that the students would have understood, "How to Add Two Matrices".

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