Show that `|[1,1+p,1+p+q],[2,3+2p,1+3p+2q],[3,6+3p,1+6p+3q]|=`

Using properties of determinants,prove the det[[1+p,1+p+q2,3+2p,1+3p+2q3,6+3p,1+6p+3q]]=1

Show that: |11+p1+p+q23+2p1+3p+2q36+3p1+6p+3q|=1

Using properties of determinants.Prove that det[[2,3+2p,1+3p+2q3,6+3p,10+6p+3q]]=1

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 the lines p_1 x + q_1 y = 1, p_2 x + q_2 y=1 and p_3 x + q_3 y = 1 be concurrent, show that the points (p_1 , q_1), (p_2 , q_2 ) and (p_3 , q_3) are colliner.

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 : [ (1) A P (2) GP (3) H P (4) none

If P=[[1,2,-3] , [3,-1,2] , [-2,1,3]], Q=[[2,3,1] ,[3,1,2] , [1,2,3]] then find the matrix R such that P+Q+R is a zero matrix

If 2x+1=15;3y-2=16 if x=p(mod 5),y=q(mod 5) then the value of p, q are (i) p=2,q=3 (ii) p=2,q=1 (iii) p=3,q=2 (iv) p=4,q=1

For any natural number p and q (i) p # q = p 3 + q 3 + 3 and p ∗ q = p 2 + q 2 + 2 and p $ q = | p − q | (ii) Max (p,q) = Maximum of (p,q) and Min (p and q) = Minimum of (p,q)The value of [(1 $ 2) # (3$ 4)]*[(5 $ 6) # (7 $ 8)] is :