HOW TO ADD TWO 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.

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

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