MATH 235 Final: MATH 235 UMass Amherst math235_fall08_html final-short
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Show all your work!: (15 points) the matrices a and b below are row equivalent (you do not need to check this fact). 1 2: find a basis for ker(a). Hint: additional calculations are not needed; use instead the rank nullity theorem: (15 points) let ~v := (cid:18) 2. Recall that the re ection t : r2 r2, with respect to the line spanned by ~v, is given by t (~x) = 2(cid:18) ~x ~v. ~v ~v(cid:19) ~v ~x. (a) show that the matrix of t , with respect to the standard basis, is. 5 (cid:18) 3 (b) let ~w := (cid:18) 1. 5 (cid:18) 3 4 to the standard basis, is b = 1 the line spanned by ~w. One can similarly show that the matrix of s, with respect. ~w ~w(cid:19) ~w ~x the re ection of r2 with respect to.
