यदि |(1+ax,1+bx,1+cx),(1+a_(1)x,1+b_(1)x,1+c_(1)x),(1+a_(2)x,1+b_(2)x,1+c_(2)x)|=A_(0)+A_(1)x+A_...

If |(1 +ax,1 +bx,1 + bx),(1 +a_(1) x,1 +b_(1) x,1 + c_(1) x),(1 + a_(2) x,1 + b_(2) x,1 + c_(2) x)| = A_(0) + A_(1) x + A_(2) x^(2) + A_(3) x^(3) , then A_(1) is equal to

Suppose a_(1)+a_(2)+a_(3)+1.3,b_(1)+b_(2)+b_(3)=2.1,c_(1)+c_(2)+c_(3)=1.6 and Delta(x)=|(1+a_(1)x,1+b_(1)x,1+c_(1)x),(1+a_(2)x,1+b_(2)x,1+c_(3)x),(1+a_(3)x,1+b_(3)x,1+c4x)| =A_(0)+A_(1)x+A_(2)x^(2)+A_(2)x^(3) , then A_(1)= _________

det[[1+ax,1+bx,1+cx1+a_(1)x,1+b_(1)x,1+c_(1)x1+a_(2)x,1+b_(2)x,1+c_(2)x the find the value of A_(1)]]=A_(0)+A_(1)x+A_(2)x^(2)+A_(3)x^(3)

The value of |(a_(1) x_(1) + b_(1) y_(1),a_(1) x_(2) + b_(1) y_(2),a_(1) x_(3) + b_(1) y_(3)),(a_(2) x_(1) +b_(2) y_(1),a_(2) x_(2) + b_(2) y_(2),a_(2) x_(3) + b_(2) y_(3)),(a_(3) x_(1) + b_(3) y_(1),a_(3) x_(2) + b_(3) y_(2),a_(3) x_(3) + b_(3) y_(3))| , is

If x in R,a_(i),b_(i),c_(i) in R for i=1,2,3 and |{:(a_(1)+b_(1)x,a_(1)x+b_(1),c_(1)),(a_(2)+b_(2)x,a_(2)x+b_(2),c_(2)),(a_(3)+b_(3)x,a_(3)x+b_(3),c_(3)):}|=0 , then which of the following may be true ?

if x,y and z are not all zero and connected by the equations a_(1)x+b_(1)y+c_(1)z=0,a_(z)x+b_(2)y+c_(2)z=0 and (p_(1)+lambdaq_(1))x+(p_(2)+lambdaq_(2))y+(p_(3)+lambdaq_(3))z=0 show that lambda =-|{:(a_(1),,b_(1),,c_(1)),(a_(2) ,,b_(2),,c_(2)),(p_(1) ,, p_(2),,p_(3)):}|-:|{:(a_(1),,b_(1),,c_(1)),(a_(2) ,,b_(2),,c_(2)),(q_(1) ,, q_(2),,q_(3)):}|

Consider the system of equations a_(1) x + b_(1) y + c_(1) z = 0 a_(2) x + b_(2) y + c_(2) z = 0 a_(3) x + b_(3) y + c_(3) z = 0 If |(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))| =0 , then the system has

The shortest distance between the lines (x-x_(1))/(a_(1)) =(y-y_(1))/(b_(1))=(z-z_(1))/(c_(1)) and (x-x_(2))/(a_(2))=(y-y_(2))/(b_(2))=(z-z_(2))/(c_(2)) is |{:(,x_(1)-x_(1),y_(2)-y_(1),z_(2)-z_(1)),(,a_(1),b_(1),c_(1)),(,a_(2),b_(2),c_(2)):}| /A Here, A refers to

consider the fourth -degree polynomial equation |{:(a_(1)+b_(1)x,,a_(1)x^(2)+b_(1),,c_(1)),(a_(2)+b_(2)x^(2),,a_(2)x^(2)+b_(2),,c_(2)),(a_(3)+b_(3)x^(2),,a_(3)x^(2)+b_(3),,c_(3)):}|=0 Without expanding the determinant find all the roots of the equation.