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Let the matrix A and B defined as A=|[3,...

Let the matrix A and B defined as `A=|[3,2] , [2,1]|` and `B=|[3,1] , [7,3]|` Then the value of `|det(2A^9 B^(-1))|=`

Text Solution

Verified by Experts

The correct Answer is:
2
`because A = [[3,2],[2,1]] and B= [[3,1],[7,3]]`
`therefore det A =-1 and det B= 2`
Now, `det(2A^(9) B^(-1)) = 2^(2) cdot det (A^(9)) cdot det (B^(-1))`
` = 2^(2) cdot (det A)^(9)cdot (det B)^(-1)`
` = 2^(2) cdot (-1)^(9)cdot (2)^(-1)=-2`
Hence, absolute value of `det ( 2A^(9)B^(-1))=2`
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