`Delta = |(a, a^2, 0),(1, 2a+b,(a+b)),(0, 1, 2a+3b)|` is divisible by`
`a.`a+b` b. `a+2b` c. `2a+3b` d. `a^2``

Prove that, |(2a, a-b-c,2a),(2b,2b,b-c-a),(c-a-b,2c,2c)|=(a + b+c)^3

If a_1b_1c_1,a_2b_2c_2 and a_3b_3c_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]| ,t h e n Delta i s divisible by 2 but not necessarily by 4 divisible by 4 but not necessarily by 8 divisible by 8 none of these

|{:(a+b,2a+b,3a+b),(2a+b,3a+b,4a+b),(4a+b,5a+b,6a+b):}|=0

Without expanding the determinant, prove that {:|( a, a ^(2), bc ),( b ,b ^(2) , ca),( c, c ^(2) , ab ) |:} ={:|( 1, a^(2) , a^(3) ),( 1,b^(2) , b^(3) ),( 1, c^(2),c^(3)) |:}

Let Delta_1=|{:(a_1,a_2,a_3),(b_1,b_2,b_3),(c_1,c_2,c_3):}| , Delta_2=|{:(6a_1,2a_2,2a_3),(3b_1,b_2,b_3),(12c_1, 4c_2,4c_3):}| and Delta_3=|{:(3a_1+b_1 , 3a_2+b_2 , 3a_3+b_3),(3b_1,3b_2,3b_3),(3c_1,3c_2,3c_3):}| then Delta_3-Delta_2=kDelta_1 , find k.

Prove |{:(1,a^2+bc,a^3),(1,b^2+ca,b^3),(1,c^2+ab,c^3):}|=-(a-b)(b-c)(c-a)(a^2+b^2+c^2)

If the roots of the equation a x^2+b x+c=0 are of the form (k+1)/k and (k+2)/(k+1) ,then (a+b+c)^2 is equal to 2b^2-a c b. a 62 c. b^2-4a c d. b^2-2a c

Let A +2B=[[1, 2, 0],[ 6,-3, 3],[-5, 3, 1] ] and 2A-B=[[2,-1, 5 ],[2,-1, 6],[ 0, 1, 2]] . Then T r(B) has the value equal to a. 0 b. 1 c. 2 d. none

If A=[(1,2,3),(2,3,1)] and B=[(3,-1,3),(-1,0,2)] , then find 2A-B .

If A=1/3|[1, 2, 2], [2, 1,-2],[a,2,b]| is an orthogonal matrix, then a=-2 b. a=2,b=1 c. b=-1 d. b=1