Home
Class 12
MATHS
Statement -1 Consider the determinant ...

Statement -1 Consider the determinant
`Delta=|{:(a_(1)+b_(1)x^(2),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,`
where `a_(i),b_(i),c_(i) in ` R (i=1,2,3) and x`in` R
Stement -2 If `|{:(a_(1),b_(2),c_(3)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}|` =0, then `Delta` =0

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|17 Videos

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|10 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|26 Videos

Similar Questions

Explore conceptually related problems

if Delta=det[[a_(1),b_(1),c_(1)a_(2),b_(2),c_(2)a_(3),b_(3),c_(3)]]

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.

The determinant |(b_(1)+c_(1),c_(1)+a_(1),a_(1)+b_(1)),(b_(2)+c_(2),c_(2)+a_(2),a_(2)+b_(2)),(b_(3)+c_(3),c_(3)+a_(3),a_(3)+b_(3))|

The value of the determinant Delta = |(1 + a_(1) b_(1),1 + a_(1) b_(2),1 + a_(1) b_(3)),(1 + a_(2) b_(1),1 + a_(2) b_(2),1 + a_(2) b_(3)),(1 + a_(3) b_(1) ,1 + a_(3) b_(2),1 + a_(3) b_(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 ?

Show that |[a_(1),b_(1),-c_(1)],[-a_(2),-b_(2),c_(2)],[a_(3),b_(3),-c_(3)]|=|[a_(1),b_(1),c_(1)],[a_(2),b_(2),c_(2)],[a_(3),b_(3),c_(3)]|

if quad /_=[[a_(1),b_(1),c_(1)a_(2),b_(2),c_(2)a_(3),b_(3),c_(3)]]

If a_(1),b_(1),c_(1),a_(2),b_(2),c_(2) "and" a_(3),b_(3),c_(3) are three digit even natural numbers and Delta=|{:(c_(1),a_(1),b_(1)),(c_(2),a_(2),b_(2)),(c_(3),a_(3),b_(3)):}| , then Delta is

Show that |{:(ma_(1),b_(1),nc_(1)),(ma_(2),b_(2),nc_(2)),(ma_(3),b_(3),nc_(3)):}|=-mn|{:(c_(1),b_(1),a_(1)),(c_(2),b_(2),a_(2)),(c_(3),b_(3),a_(3)):}|