Question

Matrix question:

Answer 1

Whats the question

Answer 2

If \[A \in \mathbb{R} ^{nxm} \] , knowing that \[\exists(A ^{T}*A)^{-1}\] and \[ P = A*(A ^{T}*A)^{-1}*A ^{T} ;\] which of these states are true? Justify your answer : \[a) (A ^{T}*A)^{-1} \] is a symmetric matrix ; \[b) (A ^{T}*A)^{-1} \] is an anti-symmetric matrix;\[c) P ^{2} = P ;\] \[d) P \] is symmetric ; \[e) P \in \mathbb{R} ^{nxn}\]

Answer 3

wooow

Answer 4

\[\large \begin{align}P^2 &=\left(A*(A ^{T}*A)^{-1}*A ^{T} \right)\left(A*(A ^{T}*A)^{-1}*A ^{T} \right) \\~\\ &=A*\left( (A ^{T}*A)^{-1}*A ^{T} A\right) *(A ^{T}*A)^{-1}*A ^{T} \\ &= A*\left( I\right) *(A ^{T}*A)^{-1}*A ^{T} \\ &=A* *(A ^{T}*A)^{-1}*A ^{T} \\ &=P\end{align}\]

Answer 5

P is also symmetric

it seems you can select more than option ?

Answer 6

Yes. You have to tell wich option is true, and which one is false.

Answer 7

Moer than one option