MAS 2103 Midterm: MAS 2103 FAU Exam 3S10
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Directions: make sure to show all necessary work to receive full credit. If you need extra space please use the back of the sheet with appropriate labeling. Good luck: let v be a vector space and suppose v1, v2, , vk v . {v1, , vk} to be linearly independent. Be sure about your quanti ers: let v be a vector space. De ne a basis for v : consider the map s : r3 r4 de ned by. S(x, y, z) = (3x 2y + 4z, x + 3y, 5x y z, x z): find as the standard matrix representation of s. then nd rref(as). Exam 3-math 3320: consider the 3 5 matrix over z7. 0 0 0 0 5: find a basis for the null space of a, find a basis for col(a), let w = {(x, y) r2|0 x2 + y2}. Determine whether w is a subspace of r3 or not.
