Grade 12Algebra
Q.17 see image...........................................................
Q.17 see image...........................................................
1 Answer
Aditya Gupta
use the fact that adj(BT)= [adj(B)]T
then let adj(B)= C
so we are given A+CT = P and AT – C= Q where P and Q are the given matrices.
note that P and Q are symmetric.
Given A+CT = P
take transpose both sides
AT+C= PT= P
also given AT – C= Q
adding 2AT= P+Q
take transpose
2A= PT+QT= P+Q
so A= (P+Q)/2 so |A|= 0 hence c is correct, obviously b is wrong.
similarly find C, you will get C= I (identity matrix)
or adjB= I
or B= |B|I So B is symmetric so A is correct
take det both sides
|B|= |B|^2
|B|=0, 1
so now you can check for D.
kindly approve :)
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