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BITSAT 2012
Exam
BITSAT
Year
2012
Subject
Mathematics
Chapter
Matrices

BITSAT 2012 · Mathematics · Matrices

Let A= [ array ll 0 & α 0 & 0 array ] and (A+I)^ 50 -50 A=[ array...

Let A=A=\left[0α00\begin{array}{ll}0 & \alpha \\ 0 & 0\end{array}\right]andand(A+I)^{50}-50 A=\left[abcd\begin{array}{ll}a & b \\ c & d\end{array}\right],find, finda b c+a b d+b c d+a c d

Options

  1. A0
  2. B-1
  3. C1
  4. DNone of these

Correct answer

A. 0

Step-by-step solution

As A2=0,Ak=0∀k≥2\mathrm{A}^{2}=0, \mathrm{ A}^{k}=0 \forall k \geq 2 Thus, (A+\quad(\mathrm{A}+\mathrm{I})50=)^{50}=\mathrm{I}+50A⇒(A++50 \mathrm{ A} \Rightarrow(\mathrm{A}+\mathrm{I})50−50A=)^{50}-50 \mathrm{ A}=\mathrm{I}∴a=1,b=0,c=0,d=1abc+abd+bed+acd=0\therefore \quad \mathrm{a}=1, \mathrm{ b}=0, \mathrm{c}=0, \mathrm{ d}=1\mathrm{abc}+\mathrm{abd}+\mathrm{bed}+\mathrm{acd}=0
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