" 32.(i) "|[a,a,x],[a,a,a],[b,x,b]|=0quad " (ii) "|[x,2,3],[4,x,1],[x,2,5]|=0

(i) Solve the equation |{:(x-2,2x-3,3x-4),(x-4,2x-9,3x-16),(x-8,2x-27,2x-64):}|=0 (ii) Prove that x = 1 is a root of the equation (ii) Prove that x=1 is a root of the following equation |{:(x+1,3,5),(2,x+2,5),(2,3,x+4):}|=0 Also find the remaining roots. (iii) If a+b+c=0 then solve |{:(a-x,c,b),(c,b-x,a),(v,a,c-x):}|=0 (iv) Solve |{:(6-x,3,3),(3,4-x,5),(3,5,4-5):}|=0

If A=[[3,2,-1],[2,-2,0],[1,3,1]],B=[[-3,-1,0],[2,1,3],[4,-1,2]] and X=A+B then find X

Find x and y, if : (i) [{:(,4,3x),(,x,-2):}] [{:(,5),(,1):}]=[{:(,y,8):}] (ii) [{:(,x,0),(,-3,1):}] [{:(,1,1),(,0,y):}]=[{:(,2,2),(,-3,-2):}]

Find x and y from the following equations: (i) [{:(,5,2),(,-1,y-1):}]-[{:(,1,x-1),(,2,-3):}] =[{:(,4,7),(,-3,2):}] (ii) [-8,x]+[y-2]=[-3,2]

If the [[x, 2,32,3, x3, x, 2]] = the [[1, x, 4x, 4,14,1, x]] = the [[0,5, x5, x, 0x, 0.5]] = 0

IF A=[{:(3,2,-1),(2,-2,0),(1,3,1):}],B=[{:(3,-1,0),(2,1,3),(4,-1,2):}] and X=A+B then find X.

If A=[[1/3,2],[0,2x-3]] , B=[[3,6],[0,-1]] and AB=I ,then x=

IF A=[{:(3,2,-1),(2,-2,0),(1,3,1):}]B=[{:(-3,-1,0),(2,1,3),(4,-1,2):}] and X=A+B then find X.

If a ,b ,c are different, then the value of |[0,x^2-a, x^3-b],[ x^2+a,0,x^2+c],[ x^4+b, x-c,0]| is a. c b. a c. b d. 0