MHB Interpreting U={A|A^2=A, A is in M22}: Not a Subspace of M22

[bbelson01]

How do I interpret the following:

U={A|A^2=A, A is an element of M22} is not a subspace of M22.

I don't quite understand what it's asking in terms of A^2=A. Thanks.

 

[MarkFL]

I have moved your new question to a new thread. We ask that new questions are not tagged onto existing threads, as this can make a thread convoluted and hard to follow. You are also more likely to get help in a more timely manner when posting new questions in new threads. :D

 

[bbelson01]

More vector subspaces

How do I interpret the following: U={A|A^2=A, A is an element of M22} is not a subspace of M22. I don't quite understand what it's asking in terms of A^2=A. Thanks.

That is all the information in the question. I can't make the jump from vectors to matrices in terms of proving subspaces.

Cheers

 

[MarkFL]

How do I interpret the following: U={A|A^2=A, A is an element of M22} is not a subspace of M22. I don't quite understand what it's asking in terms of A^2=A. Thanks.

That is all the information in the question. I can't make the jump from vectors to matrices in terms of proving subspaces.

Cheers

I have merged this duplicate posting of the question (which was posted in our high school algebra forum) with the pre-existing thread. Vectors and subspaces are university topics, most likely part of a course in linear algebra. Thus, this question is better suited here. :D

 

[Opalg]

How do I interpret the following: U={A|A^2=A, A is an element of M22} is not a subspace of M22. I don't quite understand what it's asking in terms of A^2=A. Thanks.

That is all the information in the question. I can't make the jump from vectors to matrices in terms of proving subspaces.

The properties that have to be satisfied by a subspace are the same for spaces of matrices as they are for spaces of vectors. Namely, they must be closed under the operations of addition and scalar multiplication.

In this case, the questions that you need to consider (for $2\times2$ matrices $A$ and $B$) are:
(1) If $A^2 = A$ and $B^2 = B$, is it true that $(A+B)^2 = A+B$?
(2) If $A^2 = A$ and $c$ is a scalar, is $(cA)^2 = cA$?