show that `|{:(1,,1+p,,1+p+q),(2 ,,3+2p,,1+3p+2q),( 3,, 6+3p,,1-+6p+3q):}|=1`

Show that |(1, 1+p, 1+p+q), (2, 3+2p, 4+3p+2q), (3, 6+3p, 10+6p+3q)|=1.

Using properties of determinants. Prove that |[1 ,1+p,1+p+q],[2, 3+2p,4+3p+2q],[3, 6+3p, 10+6p+3q]|=1

Using properties of determinants, prove the following: |[1,1+p,1+p+q],[2,3+2p,1+3p+2q],[3,6+3p,1+6p+3q]|=1

Show that |1 1+p1+p+q2 3+2p1+3p+2q3 6+3p 106 p+3q|=1.

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)):}|

The vertices of a triangle are (p q ,1/(p q)),(p q)),(q r ,1/(q r)), and (r q ,1/(r p)), where p ,q and r are the roots of the equation y^3-3y^2+6y+1=0 . The coordinates of its centroid are (1,2) (b) (2,-1) (c) (1,-1) (d) (2,3)

If the lines p_1x+q_1y=1,p_2x+q_2y=1a n dp_3x+q_3y=1, be concurrent, show that the point (p_1, q_1),(p_2, q_2)a n d(p_3, q_3) are collinear.

If | (a+1,a+2, a+p), (a+2, a+3,a+q), (a+3,a+4,a+r)|=0,then p ,q ,r are in:

If A = {p,q,r, s} and B = {1, 2, 3} , find which of the following is not a function from A to B? i. R 1 ​ ={(p,1),(p,2),(r,1),(s,2)} ii.R 2 ​ ={(p,1),(q,2),(r,2),(r,3)}

Show that the points P (-2, 3, 5) , Q (1, 2, 3) and R (7, 0, -1) are collinear.