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.