1 votes 1 votes if the sum of the diagonal elements of a 2x2 matrix is (-6) then the maximum possible value of determinant of the matrix is suparna kar asked Aug 9, 2018 suparna kar 2.2k views answer comment Share Follow See 1 comment See all 1 1 comment reply pankaj_vir commented Aug 9, 2018 reply Follow Share $A = \begin{bmatrix} a & b\\ c& d \end{bmatrix}$ $\left | A \right | = ad - cb$ For max $cb$ must be $0$ $\left | A \right | = ad$ $a + d = -6$ $a$ and $d$ cannot be +tive as the sum will not be -6 if $a$ is +tive or $d$ is -tive or vice versa then it will not give the maximum value [ product will be not maximum] Possible values of $a$ and $d$ $a$ $d$ $a+d$ / $a.d$ $0$ $-6$ $-6 / 0$ $-1$ $-5$ $-6 / 5$ $-2$ $-4$ $-6 / 8$ $-3 $ $-3$ $-6 / 9$ $\bigstar$ 2 votes 2 votes Please log in or register to add a comment.
2 votes 2 votes ANSWER IS +9 eyeamgj answered Aug 9, 2018 eyeamgj comment Share Follow See all 11 Comments See all 11 11 Comments reply Show 8 previous comments Deepanshu commented Aug 10, 2018 reply Follow Share yep some more conditions are required in this question 0 votes 0 votes suparna kar commented Aug 11, 2018 reply Follow Share Thank you guys for the explanation. I was not considering bc =0. Thats why making the mistake. 0 votes 0 votes Spiral commented Dec 28, 2022 reply Follow Share What if bc is negative 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes Suppose i put b=18 and c=-2 and a and d according to answers below -3 so determinant is 9-(18*-2)=45 i think this question is wrong we can find minimum not maximum Deepanshu answered Aug 9, 2018 Deepanshu comment Share Follow See all 2 Comments See all 2 2 Comments reply pankaj_vir commented Aug 9, 2018 reply Follow Share @Deepanshu: it is asking maximum possible value. 0 votes 0 votes Deepanshu commented Aug 9, 2018 reply Follow Share i dont get it 0 votes 0 votes Please log in or register to add a comment.