Question: 4. (10 points) Let V1, ... , Vn be linearly independent in a linear space C C RM, where C denotes subset of, and doesn't

4. (10 points) Let V1, ... , Vn be linearly independent in a linear space C C RM, where C denotes subset of, and doesn't exclude [ = R" . Let u1, ... , Ux be k vectors in C. Let V = VI . . . Vn and U = . . Uk . Suppose each of the k vectors uj can be written as a linear combination of the n vectors V1, ... , Vn. We saw in the previous question that U = VT for some matrix T of size n X k and that null(U) = null(T). Then if in addition, U1, ... , Uk are linearly independent, then A. U has a pivot in each column T has a pivot in each column B. VC. k and n can be any two numbers

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