Evaluate the determinant by using diaganals

C. 26

Step-by-step explanation:

The question is on finding determinant of 3×3 matrix

General formulae is given by

if we have matrix (a  b  c)

                             (d  e  f)  

                              (g  h  i ) then the determinant will be given by

a× D( e f) - b × D (d f)  + c× D ( d e)

       (h  i)              (g i)              (g  h)

where D is the determinant

Evaluate

(a  b  c)     (-4  3  3)

(d  e  f)  =  (3  0  2)  = -4 ×D(0 2)  - 3×D (3 2) + 3×D (3 0)

 (g  h  i )     (3  1   1)                (1   1)           (3  1)           (3  1)

= -4 × {(I×0)-(1×2)} -3 {(3×1)-(3×2)} + 3 { (1×3)-(3×0)}

= -4 ×{-2} - 3×{-3} +3× {3}

=8+9+9= 26

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50