Question Number 100664 by bobhans last updated on 28/Jun/20

A matrix 2x2 & B =  (((−2    3)),((  2      4)) )  such that   A^T B+3A^T  =  (((   5    4)),((−1   1)) )  so find det(4A^(−1) )

Answered by bramlex last updated on 28/Jun/20

A^T (B+3I) =  (((   5    4)),((−1   1)) )  det(A^T ) = det(A) = ( determinant (((   5    4)),((−1   1)))/(det(B+3I)))  = (9/ determinant (((1     3)),((2     7)))) = (9/1) = 9  therefore det(4A^(−1) ) = ((16)/(det(A))) = ((16)/9)