1. ## Invertible formulas problem

Determine which of the formulas hold for all invertible matrices and

A. is invertible
B.
C.
D.
E.
F. is invertible

I have to select which of the above are true. I thought I was right in picking A, C and F. However, I was apparently wrong.

Any help is greatly appreciated. Thanks in advance!

2. Originally Posted by elven06
Determine which of the formulas hold for all invertible matrices and

A. is invertible
B.
C.
D.
E.
F. is invertible

I have to select which of the above are true. I thought I was right in picking A, C and F. However, I was apparently wrong.

Any help is greatly appreciated. Thanks in advance!

A and E are the only true ones. Now try to show, by counterexamples, why.

Tonio

3. Originally Posted by tonio
A and E are the only true ones. Now try to show, by counterexamples, why.

Tonio
Is this some sort of rule? You seemed to figure it out really fast. I have another problem of a similar nature, I don't really know how to go about tackling it:

Which of the following sets are subspaces of ?

A.
B. arbitrary number
C. arbitrary number
D. arbitrary number
E.
F.

4. For the first question a lot of them can be solved by remembering some Matrix multiplication rules. ABC = (AB)C = A(BC). However AB does not equal BA.

For the second question remember the requirements for a subspace: Does the space contain the zero vector? If V and U are in the subspace then is V+U is also in the subspace? for some scalar r if U is in the subspace is rU in the subspace? If you answered yes to all of the previous questions then it is a subspace. If you answered no to any one of them it is not.