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If A= [ array ll a & b c & d array ] (where .b c 0 ) satisfies the equations x^2+k=0 , then

Options

  1. Aa+d=0
  2. Bk =-| A |
  3. Ck=|A|
  4. DNone of these

Correct answer

C. k=|A|

Step-by-step solution

We have A^2= [ array ll a & b c & d array ] [ array ll a & b c & d array ]= [ array ll a^2+b c & a d+d b a c+c d & b c+d^2 array ] As A satisfies, x^2+k=0, A^2+k I=0 [ array cc a ^2+ bc + k & ( a + d ) b ( a + d ) c & bc + d ^2+ k array ]=0 a^2+b c+k=0=b c+d^2+k=0 and (a+d) b=(a+d) c=0 As b c 0, b 0, c 0 a+d=0 a=-d ( A ) Also, k=- (a^2+b c )=- (d^2+b c )=-((-a d)+b c)=|A| (C)

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