M-221 Midterm: MATH 221 Montana State Exam3TH
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Show complete and proper work for full credit in all problems. I am the only person that you can ask questions to as well: given the system. Find the general solution, ~x = ~xp + ~xh, where ~xp is a particular part and ~xh is the homogeneous part, such that ~xp row(a) and ~xh null(a). Note: this is possible since, theorem 4. 28 states that r3 = (row(a)) (null(a)) and row(a) null(a). And, from part(b) of theorem 4. 26 we get that every vector ~x r3 can be uniquely written as. Find this unique representation of ~xp r3. ~xnp null(a). (e) now we apply theorem 4. 26 to the general solution, ~x r3. ~ xp = and ~ xh : consider the subspace u = span{~u1, ~u2, ~u3} of r4, where. 3 (a) (6pts) use the gram-schmidt process from exercise 4. 16 to nd an orthogonal basis, {~v1, ~v2, ~v3}, of. Answer: (b) (2pts) verify that this basis is orthogonal.
