MATH 2090 Problem Workshop Week 3
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
MATH 2090 Problem Workshop Week 3
1. Determine the dimension of:
(a) The diagonal n × n matrices.
(b) The symmetric n × n matrices.
(c) The polynomials in such that p(2) = 0.
(d) The vectors of the form (a, b, c, d) where d = 2c = 4b = 8a.
2. For the bases B = {6 + 3x, 10 − 2x} and S = {4 + x, 6 − x}:
(a) Compute the transition matrix from B → S.
(b) Compute the transition matrix from S → B.
(c) Compute the coordinate vector [p]B if p(x) = 5 + 9x.
(d) Compute [p]S.
3. In class we came up with a matrix procedure to compute the transition matrix for two bases in . Determine a similar procedure for and use it to compute the previous question
4. Determine bases for the row-space, column space, null space, rank and nullity of the matrix
5. Let S = {v1, v2, . . . , vr} and suppose W = span(S). Show that if x is orthogonal to all vectors in S, then x is orthogonal to all vectors in W.
2021-10-28