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Problem 04 (a) What can be said about the four fundamental subspaces when

`Ax=b`

has an unique solution, no solution, and infinitely many solutions? (b) Find the basis and dimension for each of the spaces formed by the following matrices. Also explain why they are vector spaces. (i) All diagonal

`3\times 3`

matrices. (ii) All symmetric

`3\times 3`

matrices