Construct a 3\times3 matrix A, with nonzero entries, and a vector b in

Tabansi 2021-10-24 Answered
Construct a 3×3 matrix A, with nonzero entries, and a vector b in R3 such that b is not in the set spanned by the columns of A.
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Expert Answer

Sally Cresswell
Answered 2021-10-25 Author has 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.
x1[111]+x2[111]+x3[111]=[x1+x2+x3x1+x2+x3x1+x2+x3]
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:
A=[111111111]
and
b=[123]

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