Home
Class 12
MATHS
Consider two matrices A=[[a,b],[b,a]] an...

Consider two matrices `A=[[a,b],[b,a]]` and `B=[[a,-b],[-b,a]]` then the value of `sum_(n=1)^10 |(AB)^n|` is (i) 10`(a^2-b^2)` (ii)`(((a^2-b^2)^22)-((a^2-b^2)^2))/((a^2-b^2)^2-1)` (iii)`(((a^2-b^2)^11)-((a^2-b^2)^2))/((a^2-b^2)-1)` (iv) 55`(a^2-b^2)`

Promotional Banner

Similar Questions

Explore conceptually related problems

If A=[[1,-1],[ 2,-1]] and B=[[a,1],[b,-1]] and (A+B)^2=A^2+B^2, then find the value of a and b .

If A_i= [ [a^i, b^i] , [b^i, a^i]] and if |a|<1, |b|<1 then sum_(i=1)^oo det(A_i) = (A) a^2/(1-a)^2- b^2/(1-b)^2 (B) a^2/(1-a)^2+ b^2/(1-b)^2 (C) a^2/(1+a)^2- b^2/(1+b)^2 (D) (a^2-b^2)/[(1-a^2)(1-b^2)]

If a=2 and b=-2, find the value of : (i) a^(2)+b^(2) (ii) a^(2)+ab+b^(2) (iii) a^(2)-b^(2)

If A=[[1,-1],[2,-1]] , B=[[a,1],[b,-1]] and (A+B)^(2)=A^(2)+B^(2) ,then find the values of a and b

If A=[[a,b],[-1,2]],B=[[1,1],[2,4]] and (A+B)(A-B)=A^(2)-B^(2) , then the value of a+b equals

1+a^(2)-b^(2),2ab,-2b2ab,1-a^(2)+b^(2),2a2b,-2a,1-a^(2)-b^(2)]|=(1+a^(2)+b^(2))^(3)

|(1+a^(2)-b^(2), 2ab, -2b),(2a, 1 -a^(2)+b^(2),2a),(2b, -2a, 1-a^2-b^2)|=(1 + a^2 + b^2)^(3) .

If (x+1)/(x-1)=(a)/(b) and (1-y)/(1+y)=(b)/(a), then the value of (x-y)/(1+xy) is (2ab)/(a^(2)-b^(2)) (b) (a^(2)-b^(2))/(2ab) (c) (a^(2)+b^(2))/(2ab) (d) (a^(2)-b^(2)backslash)/(ab)

If A=[[1,-1],[2,-1]],B=[[a,1],[b,-1]] and (A+B)^(2)=A^(2)+B^(2) , the value of a+b is