I’m enjoying Linear Algebra for Beginners and am using it to refresh stuff I should have learned properly in about 1967.
In Chapter 9, Problem Set, Sets that are not vector spaces, problem 1, you give us the set of 2×2 invertible matrices with the operations matrix multiplication and scalar multiplication.
I tried to find an excption to the closure requirement without success. I peeked at the your solution and you give an example of two invertible matrices whose matrix sum is not invertible.
Shouldn’t we be seeking a pair whose matrix product or scalar product are not invertible?
Richard,
I’m enjoying Linear Algebra for Beginners and am using it to refresh stuff I should have learned properly in about 1967.
In Chapter 9, Problem Set, Sets that are not vector spaces, problem 1, you give us the set of 2×2 invertible matrices with the operations matrix multiplication and scalar multiplication.
I tried to find an excption to the closure requirement without success. I peeked at the your solution and you give an example of two invertible matrices whose matrix sum is not invertible.
Shouldn’t we be seeking a pair whose matrix product or scalar product are not invertible?
Thanks
Pat
Hi Pat,
You can check any of the vector space properties, and if at least one fails, then you know the set is not a vector space.
That’s so cool, Richard, that you are offering help in the comments for us readers! thank you!