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a matrix X has (a+b) rows and (a+2) columns, while the matrix Yhas (b+1)rows and (a+3)columns both XY and YX exist. find a and b

a matrix X has (a+b) rows and (a+2) columns, while the matrix Yhas (b+1)rows and (a+3)columns both XY and YX exist. find a and b 

Grade:12

1 Answers

Arun
25750 Points
5 years ago
if XY exist , then number of columns in X = number of rows in Y
therefore
a+2=b+1
a - b = -1 .......(1)
if YX exist , then number of columns in Y = number of rows in X
a+3 = a+b
therefore b = 3
from eq(1):
a - 3 = -1
a = 2
the number of rows in X = 2+3 = 5
the number of columns in X = 2+2 = 4
the number of rows in Y = 3+1 = 4 
the number of columns in Y = 2+3 =5
thus order of XY is 5*4 and order of YX is 4*5
thus both are of different type.

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