Let be finite dimensional linear spaces and let be a basis for and let be a basis for . Let . Construct a basis for .
I'm probably making this way harder than it really is. The only idea I came up with was
But I know that's wrong....
Let be finite dimensional linear spaces and let be a basis for and let be a basis for . Let . Construct a basis for .
I'm probably making this way harder than it really is. The only idea I came up with was
But I know that's wrong....
Think of an example. Take your favourite 2-dimensional vector space and cross it with your favourite 3-dimensional vector space. Can you think of a basis for this new space?
Also, I would recommend contemplating how many elements your new basis will have. Hopefully the example will make this clear, but if not...think about it...