Question: Consider the matrix A = [3 1 2] 452 764 (a) Derive the set of vectors N(A) = {x: Ax = 0} where 0

Consider the matrix A = [3 1 2] 452 764 (a) Derive

Consider the matrix A = [3 1 2] 452 764 (a) Derive the set of vectors N(A) = {x: Ax = 0} where 0 denotes the matrix with all zeroes. (3 points) (b) What is the set N(A) called? Does it form a vector space in general? Justify your answer. (4 points) (c) Derive the set of vectors C(A) points) = {b: Ax - b has a solution}. (3 (d) What is the set C(A) called? Does it form a vector space in general? Justify your answer. (4 points) (e) Calculate the eigenvalues of A. Find the determinant of A without calculating it explicitly. (3 points)

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