Q. 214.7( 7 Votes )

If find x and y such that A2 + xI = yA.

Answer :

Given : A2 + xI = yA.


A is a matrix of order 2 x 2


To find : x and y


Formula used :



Where cij = ai1b1j + ai2b2j + ai3b3j + ……………… + ainbnj


If A is a matrix of order a b and B is a matrix of order c d ,then matrix AB exists and is of order a d ,if and only if b = c


A2 is a matrix of order 2 x 2


A2 = = =


A2 = =


A2 =


xI = =


xI =


A2 + xI = + = =


A2 + xI =


yA = y =


yA =


It is given that A2 + xI = yA,


=


Equating similar terms in the given matrices,


16 + x = 3y and 8 = y,


hence y = 8


Substituting y = 8 in equation 16 + x = 3y


16 + x = 3 × 8 = 24


16 + x = 24


x = 24 – 16 = 8


x = 8


x = 8, y = 8


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