Home
Class 12
MATHS
If A is an idempotent matrix satisfying ...

If `A` is an idempotent matrix satisfying `(I-0.4A)^(-1)=I-alphaA` where `I` is the unit matrix of the same order as that of `A` then the value of `alpha` is

Text Solution

Verified by Experts

`because ` A is idempotent matrix
`therefore A^(2) = A`,
similarly `A = A^(2) = A^(3) =A^(4) =... = A^(n)` …(i)
Now, `(A+I)^(n) = (I+A)^(n)`
`I+""^(n)C_(1)A+""^(n) C_(2) A^(2)+""^(n)C_(3) A^(3) +...+ ""^(n) C_(n) A^(n) `
`I+(""^(n)C_(1)+""^(n) C_(2) +""^(n)C_(3) +...+ ""^(n) C_(n)) A ` [ from Eq.(i)]
`I+(2^(n)-1)A`
Hence, `(A+I)^(n) = I + (2^(n)-1) A, AA n in N.`
Promotional Banner

Similar Questions

Explore conceptually related problems

If B is an idempotent matrix, and A=I-B , then

If A is an idempotent matrix and I is an identify matrix of the Same order, then the value of n, such that (A+I)^n =I+127A is

If I is a unit matrix of order 10 , then the determinant of I is equal to

If A(adiA)=5I where I is the identity matrix of order 3 , then |adjA| is equal to

Matrix A such that A^(2)=2A-I , where I is the identity matrix, then for n ge 2, A^(n) is equal to

If A = [{:(cos 2thet,,-sin 2theta),(sin 2theta,, cos 2theta):}] and A + A^(T) = 1 , where I is the unit matrix of 2 xx 2 & A^(T) is the transpose of A. then the value of theta is equla to

If A is a matrix of order 3, such that A(adj A) = 10 I, then find |adj A| =

If A is a matrix of order mxx m such that A^(2) +A + 2I = O , then