How to Check Answers
In the review last night, the professor talked a lot about how being able to check your answers is extremely important, both because it helps you do the problem correctly, and because it shows the grader you know what you're doing. He said that even if you get the answer wrong, if you can demonstrate that you checked it and write something like "my check shows that my answer is incorrect, but I don't have time to fix it" you're likely to get as much as 9/10 on the problem. So! It would be useful to know how to check your solutions. I will start us off: 1) To check if your matrix/basis is orthogonal, each vector dotted with each of the other vectors should be 0.
carlintou: June 4, 2015, 1:19 p.m.
You can check an eigenvalue and it's corresponding vector in that basis by using the equation Av=(lambda)v
alexwang0518: June 4, 2015, 1:36 p.m.
Check inverses by (A)(A)^-1=I
justinKennedy: June 4, 2015, 5:19 p.m.
Matrix is also orthogonal if $A^{T}A= I_{n} $ Also, regarding change of basis problems, $x= S*[x]_{B} $ where S holds the basis vectors [v1 v2] and $[x]_{B} $ describes the location of x in terms of the basis vectors ( $x = c_{1}v_{1} + c_{2}v_{2} , [x]_{B} = [c_{1} c_{2}] $ as vertical column vector ). With this as well, $ [T(x)]_{B} * S = T(x) $