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Literature & Language
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Math Problem
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# Linear Algebraic Problems (Math Problem Sample)

Instructions:

Determine if matrix a is idempotent. A square matrix A is idempotent if A2=A.
Prove that if A is an n×n matrix that is idempotent and invertible.
A square matrix A is idempotent if A2=A.
Prove that if A is an n×n matrix that is idempotent and invertible, then A is the identity.A square matrix A is idempotent if A2=A.
Prove that if A is an n×n matrix that is idempotent and invertible, then A is the identity.
How do i prove this?
How do i prove this?
How do i prove this?
Find whetheR matrix A iS invertible.
Find eigen value corresponding to matrix A

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Content:

Linear Algebra Problem
* Since a is idempotent, we have
A2 = A
(I – A)2 = I2 + A2 – 2IA
(I – A)2 = I + A -A
(I – A)2 = I – A
Implying that I – A is idempotent
* Since A is invertible, A-1 exist
A2 = A
Multiply both sides by A-1
A-1(AA) = A-1A
(A-1A)A = A-1A
IA = I
A = I
* Let λ be the eigen value of A corresponding to the vector
Then, Av = λv
A2v = λv
A(λv) = λv
A(Av) = λv

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