A valid argument is one in which the conclusion must be true if the premises are both true. In this invalid argument, you have a conclusion that does not have to follow from the premises.
Your premises are:
- All students are brilliant.
- She is brilliant.
Your conclusions is:
- Therefore she is a student.
But there could be other types of brilliant people -- your premises do not preclude that possibility.
To make this argument valid, simply change the first premise. If you change the first premise as follows, then the conclusion will have to be true and the argument will be valid.
- Only students are brilliant.
Since she is a student and only students are brilliant, she must be a student. This is a valid argument.