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If A= [ array l 1 2 3 array ] , then what is value of det (I+A A^ ) , where I is the 3 3 identity matrix?

Options

  1. A15
  2. B6
  3. C0
  4. D-1

Correct answer

A. 15

Step-by-step solution

Since, I + AA' aligned & = [ array lll 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 array ]+ [ array l 1 2 3 array ] [ array lll 1 & 2 & 3 array ] & = [ array lll 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 array ]+ [ array lll 1 & 2 & 3 2 & 4 & 6 3 & 6 & 9 array ]= [ array ccc 2 & 2 & 3 2 & 5 & 6 3 & 6 & 10 array ] aligned Now, | I + AA ^ |=2(50-36)-2(20-18)+3(12-15)=15

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