[(1)/(231)," (iii) "3.5bar(2)]

Find the rational number whose decimal expansion is given below : (i) 0.bar(3) (ii) 0.bar(231) (iii) 3.bar(52)

If A=[[0,1,3],[1,2,x],[2,3,1]] and A^(-1)=[[(1)/(2),-4,(5)/(2)],[-(1)/(2),3,-(3)/(2)],[(1)/(2),y,(1)/(2)]] . Find x,y

Let A = {:[( 1,2,1),(2,3,1),(1,1,5) ]:} Verify that (A^(-1) )^(-1) =A

If A=[(1,2,5),(2,3,1),(-1,1,1)] verify that A^(-1)A="AA"^(-1)=I

Find the inverse (if it exists) of the following: (i) [{:(-2,4),(1,-3):}] (ii) [{:(5,1,1),(1,5,1),(1,1,5):}] (iii) [{:(2,3,1),(3,4,1),(3,7,2):}]

Consider the matrices A=[(2,1,3),(2,3,1),(1,1,1)] and B=[(-1,2,3),(-2,3,1),(1,1,1)] Find A+B.

The rank of [(1,4,-1),(2,3,1),(1,1,2)] is

Prove that the following four points are coplanar. i) 4bar(i)+5bar(j)+bar(k), -bar(j)-bar(k), 3bar(i)+9bar(j)+4bar(k), -4bar(i)+4bar(j)+4bar(k) ii) -bar(a)+4bar(b)-3bar(c), 3bar(a)+2bar(b)-5bar(c), -3bar(a)+8bar(b)-5bar(c), -3bar(a)+2bar(b)+bar(c)" ("bar(a), bar(b), bar(c) are non-coplanar vectors) iii) 6bar(a)+2bar(b)-bar(c), 2bar(a)-bar(b)+3bar(c), -bar(a)+2bar(b)-4bar(c), -12bar(a)-bar(b)-3bar(c)" ("bar(a), bar(b), bar(c) are non-coplanar vectors)

Show that the points (1,2,3), (2,3,1) and (3,1,2) from an equilateral triangle.