MATH 308 Final: MATH 308 UW 308G Sp16 Final Solution
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Math 308g spring 2016 solutions to the final exam. Rank-nullity theorem it does not change the nullity. ) 2. (a) for example, t : r2 r2 given by the matrix (cid:20) 2 1. 0 (b) the one above works. (c) for example, 0 2(cid:21) , b = (cid:20)2 1 (d) not possible since an orthogonal set has to be linearly independent. (e) 2 (cid:21) = (cid:20)6 3 5 2 10 3 + 10 2. 3 3 3 2 5 3 + 6 2 (cid:21) : answer the questions below using the already computed reduction of the matrix. 0 (a) from the reduced matrix x4 = 3, x3 = 0, x2 = t, x1 = 2t so the solution is given by x = The rst part is the homogeneous solution and the second part without the t is the particular solution. (b) the column space of the matrix a has dimension 3 and a basis is given by.
