KVPY SX SB Exam 2018 Question Paper

Question : 1 of 120

Marks: +1, -0

PART-I MATHEMATICS

Suppose

\A = [\table a,b;c,d]

is a real matrix with nonzero entries, ad – bc = 0, and

\A^2 = \A

. Then a + d equals

Solution:

ad=bc⇒a/b=c/d=k

⇒a=bk,c=dk

\A^2 = [\table a,b;c,d]. [\table a,b;c,d]

=[\table a^2+bc,ab+bd;ac+cd,bc+d^2]

\A^2=\A

∴a^2+bc=a;b(a+d)=b

⇒a+d=1

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