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!
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.
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.