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Construct a 3×3 matrix A, with nonzero entries, and a vector b in R^3 such that b is not in the set spanned by the columns of A. Choose the correct answer below.

Construct a 3×3 matrix A, with nonzero entries, and a vector b in R^3 such that b is not in the set spanned by the columns of A. Choose the correct answer below.

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Construct a 3×3 matrix A, with nonzero entries, and a vector b in R^3 such that b is not in the set spanned by the columns of A. Choose the correct answer below.

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A vector b is a linear combination of the columns of a matrix A if and only if the equation Ax = b has at least one solution. Choose the correct answer below. A. True. The equation Ax = b has the same solution set as the equation x1a1 + x2a2 +...+xnan = b B. True. The equation Ax = b is unrelated to whether the vector b is a linear combination of the columns of a matrix A. C. False. If the matrix A is the identity matrix, then the equation Ax = b has at least one solution, but b is not a linear combination of the columns of A. D. False. If the equation Ax = b has infinitely many solutions, then the vector b cannot be a linear combination of the columns of A.
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