[" Determinants "],[qquad [" Without expanding the determinant at any stage,prove that "],[[x-3,x-4,x-alpha],[x-2,x-3,x-beta],[x-1,x-2,x-gamma]]]

If alpha,beta,gamma are in A.P. then show that , |[x-3,x-4,x-alpha],[x-2,x-3 ,x-beta],[x-1,x-2,x-gamma]|=0

Show that [[x-3,x-4,x-alpha],[x-2,x-3,x-beta],[x-1,x-2,x-gamma]]=0 where alpha,beta,gamma are in AP

Without expanding, evaluate the determinants : |(2,3,4),(5,6,8),(6x,9x,12x)|

Show that |{:(x-3,x-4,x-alpha),(x-2,x-3,x-beta),(x-1,x-2,x-gamma):}|=0,where" "alpha,beta,gamma are in A.P

Without expanding a determinant at any stage, show that abs((x^2+x ,x+1 , x-2),(2x^2+3x-1 ,3x , 3x-3) , (x^2+2x+3, 2x-1 ,2x-1))=xA+B ,where A and B are determinant of order 3 not involving xdot

Without expanding a determinant at any stage, show that abs((x^2+x ,x+1 , x-2),(2x^2+3x-1 ,3x , 3x-3) , (x^2+2x+3, 2x-1 ,2x-1))=xA+B ,where A and B are determinant of order 3 not involving xdot

Without expanding a determinant at any stage, show that |{:(x^(2)+x, x+1, x+2),(2x^(2) +3x-1, 3x, 3x-3),(x^(2) +2x+3, 2x-1, 2x-1):}|=xA+B where A and B are determinants of order 3 not involving x.

Without expanding a determinant at any stage, show that | |x^2+x ,x+1 , x+2|,|, 2x^2+3x-1, 3x , 3x-3 | , | x^2+2x+3, 2x-1 ,2x-1||=x A+B ,w h e r eAa n dB are determinant of order 3 not involving xdot

Without expanding show that the determinant |(1,a,a^2),(-1,2,4),(1,x,x^2)| has a factor (X-a)

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(x+4,2x,2x),(2x,x+4,2x),(2x,2x,x+4):}|=(5x+4)(4-x)^2