Tabansi

2021-10-24

Construct a $3\times 3$ matrix A, with nonzero entries, and a vector b in $\mathbb{R}}^{3$ such that b is not in the set spanned by the columns of A.

Sally Cresswell

Skilled2021-10-25Added 91 answers

For the matrix A in the result, any vector in the span of the column vectors is of the form on the left.

After multiply the scalars and adding the vectors, we get a vector of this form. Notice that all the entries vector are equal. Since the entries in vector b are not all same, 1,2,3,b cannot be in the span of the column vectors.

Result:

and

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