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If A=\left[ \begin{array}{rrr}{1} & {2} & {2} \\ {2} & {1} & {-2} \\ {a} & {2} & {b}\end{array}\right] is a matrix satisfyingthe equation AA^T=91, where l is 3x3identity matrix, then the ordered pair(a, b) is equal tob) is equal to |
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Answer» A= 1 2 2 A^T=1 2 a 2 1 -2 2 1 2 a 2 b 2 -2 bA*A^T=1+4+4 2+2-4 a+4+2b =9 0 0 2+2-4 4+1+4 2a+2-2b 0 9 0 a+4+2b 2a+2-2b a^2+4+b^2 0 0 9a+2b+4=02a-2b+2=0a+2b+4+2a-2b+2=03a+6=0so a=-2-2+2b+4=02b=-2b=-1 |
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