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....

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- August 25th 2010, 05:10 PMmathematicalbagpiperBasis of a Cartesian product
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.... - August 26th 2010, 12:21 AMSwlabr
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... - August 26th 2010, 01:47 AMSwlabr
Don't just give the answer away! Rule 14!