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1-How do you determine if a set of vectors [in matrix form] span a region?

-Do you set the given matrix set to arbitary numbers and see if

there is a unique, infinite, or no solution?

ie, set a 4X4 matrix = to [a b c d] and determine the type of solution?

2. How do you find a basis for the kernel of the linear map L : R^4 goes to

R4 corresponding to multiplication of a given matrix?

-Do you do the same thing as above, but set the given matrix equal to

zero to find the kernal and after you find the kernal, do you find the

basis?

3. How do you find a basis for the range of this same map?

Do you find the range, then the basis?

I think if I understand these concepts, I can do the homework. Any assistance would be appreciated.

Thanks in advance!