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Question

# Following questions contains statements given in two columns, which have to be matched. The statements in Column−I are labelled as A, B, C and D while the statements in Column−II are labelled as p, q, r and s. Any given statement in Column−I can have correct matching with ONE statement in Column−II.

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Solution

## A) Given |A|=162 and A is a square matrix of order 3.Now, det{A3}=133|A| (Because when we divide matrix A by 3, each element of matrix gets divided by 3. So when we take determinant of such matrix , we get 13 common from each row (or column). So, 133 multiplied by |A| )⇒det{A3}=16227=6B) Given A2=AAlso (I+A)5=I+λA⇒5C0+5C1A+5C2A2+5C3A3+5C4A4+5C5A5=I+λA⇒I+(5+10+10+5+1))A=I+λA⇒λ=31⇒2λ+17=9 C) Given A=[4325] ⇒A2=[4325][4325]⇒A2=[22271831]Also given A2−xA+yI=O ⇒[22271831]−[4x3x2x5x]+[y00y]=[0000]⇒[22−4x+y27−3x18−2x31−5x+y]=[0000]⇒22−4x+y=0;18−2x=0;27−3x=0;31−5x+y=0Solving these, we get x=9,y=14⇒y−x=5

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