Null & Column Spaces and Linear Xformations

Note that here multiplication is multiplication of vector and scalar and sum is sum of vectors) so $$ b = \sum_{i=0}^n \alpha_i v_i $$ which $v_i$'s are columns of b and

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Math 22 – Linear Algebra and its applications

Yes. The answer to your problem is either one or two, but is clearly two as the entries in the 1st and 4th positions are independent of one another. It is no more than the