Question: Please solve problem 3 Problem 3 (15 points) We have two linear functions f : R' - R' and g : R3 - R4. The

Please solve problem 3

Problem 3 (15 points) We have two linear functions f : R' - R' and g : R3 - R4. The images of both functions have dimension 3. 1. What are the dimensions of the kernels of f and g? Is either function invertible? 2. What are the row and column ranks of the matrices A and B, where f(X) = Ax and g(x) = BX? 3. What are the nullities of A and B? Is either matrix invertible? 4. What are the complementary subspaces of Ker f and Im f? 5. What are the dimensions of the complementary subspaces of Ker g and Im g

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