InterviewSolution
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InterviewSolution
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If A and B are two non-singular matrices of order 3 such that `A A^(T)=2I` and `A^(-1)=A^(T)-A`. Adj. `(2B^(-1))`, then det. (B) is equal toA. 4B. `4sqrt(2)`C. 16D. `16sqrt(2)` |
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Answer» Correct Answer - D `A A^(T)=2I` ...(1) `implies |A|^(2)=8` Now, `A^(-1)=A^(T)-A" adj."(2B^(-1))` ...(2) Multiplying with A, we get `I=A A^(T)-A^(2)"adj."(2B^(-1))` `:. I=2I-A^(2)"adj."(2B^(-1))` `implies A^(2)"adj." (2B^(-1))=I` `implies |A^(2)||"adj." (2B^(-1))|=1` `implies 8|2B^(-1)|^(2)=1` `implies 8. 64/(|B|^(2))=1` `implies |B|^(2)=64xx8` `:. |B|= pm (8xx2sqrt(2))= pm 16 sqrt(2)` |
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