Question: In this problem, you are to work with the following matrix 1 2 1 5 16 3 13 1 4 2 9 A =

In this problem, you are to work with the following matrix 1 2 1 5 16 3 13 1 4 2 9 A = a. Determine the

In this problem, you are to work with the following matrix 1 2 1 5 16 3 13 1 4 2 9 A = a. Determine the number of pivots, identify the basic variables, and identify the free variables. b. Determine whether the set {a, a2, a3, a4}, which is the set of the column vectors of A, spans a point, a line, a plane, a 3-D volume, or a 4-D volume. c. For each of the sets S = {a, a2}, S = {a2, a3}, S3 {a, a2, a3}, and S4 = {a, a2, a4}, determine whether it is a linearly dependent set or a linearly independent set. e. Find a new vector a5 so that the new set S5 independent. = = {a1, a2, a5} is linearly

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a To determine the number of pivots we need to perform Gaussian elimination on matrix A and count the number of nonzero rows at the end The pivots will be the leading nonzero entries in each row Perfo... View full answer

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