A=[[2,1],[4,1]]; B=[[3,4],[2,3]] & c=[[3...

`A=[[2,1],[4,1]]; B=[[3,4],[2,3]]` & `c=[[3,-4],[-2,3]]`, `tr(A)+tr[(ABC)/2]+tr[(A(BC)^2)/4]+tr[(A(BC)^2)/8]+.....oo` is:

Text Solution

Verified by Experts

`A = [[2,1],[4,1]]`
`B = [[3,4],[2,3]]`
`C = [[3,-4],[-2,3]]`
`:. BC = [[3,4],[2,3]][[3,-4],[-2,3]] = [[9-8,-12+12],[6-6,-8+9]] = [[1,0],[1,0]] = I`
`:. (BC)^2 = (BC)^4 =... = I`
So, required expression becomes,
`tr(A) + tr[A/2]+tr[A/4]+...oo`
Now, `tr(A) = `Sum of diagonals `= 2+1 = 3`
...

Similar Questions

Explore conceptually related problems

Let three matrices A = [[2,1],[4,1]],B=[[3,4],[2,3]]and C= [[3,-4],[-2,3]], then tr (A) + tr ((ABC)/2)+tr((A(BC)^(2))/4) + tr ((A(BC)^(3))/8) +...+infty equals to

Let three matrices A=[(2 ,1),( 4, 1)]; B=[(3, 4),( 2, 3)] and C=[(3,-4),(-2,3)], then tr(A) + tr((ABC)/2) + tr((A(BC)^2)/4) + tr((A(BC)^3)/8) + ......∞ (a)6 (b) 9 (c) 12 (d) None of these

consider three matrix A=[[2 , 1] , [4 , 1]] , B=[[3 , 4] , [2 , 3]] , C=[[3 , -4] , [-2 , 3]] then the value of sum of tr(A)+tr((ABC)/2)+tr((A(BC)^2)/4)............

Consider three matrices A=[(3,1),(6,1)],B=[(3,4),(2,3)] and C=[(3,-4),(-2,3)] then the value of tr(A)+tr((ABC)/2)+tr((A(BC)^(2))/4)+tr((A(BC)^(3))/8)+ …………..

Consider three matrices A=[(2,1),(4,1)], B=[(3,4),(2,3)] and C=[(3,-4),(-2,3)]. Then the value of the sum tr(A)+tr((ABC)/2) +tr((A(BC)^2)/4)+tr((A(BC)^3)/8)+.......+oo is (A) 6 (B) 9 (C) 12 (D) none of these

Consider three matrices A=[(2,1),(4,1)], B=[(3,4),(2,3)] and C=[(3,-4),(-2,3)]. Then ghe value of the sum tr(A)+tr((ABC))/2 +tr((ABC)^2)/4+tr((ABC)^3)/2+.......+oo is (A) 6 (B) 9 (C) 12 (D) none of these

If tr(A)=3,tr(B)=5 then tr(AB)=

`A=[[2,1],[4,1]]; B=[[3,4],[2,3]]` & `c=[[3,-4],[-2,3]]`, `tr(A)+tr[(ABC)/2]+tr[(A(BC)^2)/4]+tr[(A(BC)^2)/8]+.....oo` is:

Text Solution

Similar Questions

Recommended Questions