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Matrix Algebra - Linearly independent

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Suppose A is a 5 by 4 matrix, b is a vector in R^5, and p = [-2 1 0 4] is a solution of the equation Ax = b. For each of the following statements, determine whether the statement is true, false, or cannot be determined from the information given.

(a) The vector b is in the span of the columns of A.

(b) The equation Ax = b has an infinite number of solutions.

(c) The columns of A form a linearly dependent set of vectors.

(d) The equation Ax = 2b has a solution.

(e) The set of vectors {A1, A2, A3, A4, b}, where A1, A2, A3, A4 are the columns of A, is a linearly independent set.

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This posting, which is provided in an attached Word document, determines whether each of the statements is true or false and provides brief explanation for these responses.

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Assume , where are 4 columns of .
(a) Answer: True
Since is a solution of , then . Then we have
. Then is in the span of columns of ...

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