introduction To Linear Transformations (sec. 1.8 Linear Algebra book by Lay)

I have three homework problems that I got stuck on while, trying to solve. I'd really appreciate it if anyone could help me with these. Here they are

For # 14 & 16 use a rectangular coordinate system to plot u= [vertical: 5 2]

, v=[vert: -2 4], and their images under the given transformation T. (Make a large sketch for each exercise.) Describe geometrically what T does to each vector **x **in R^2.

#14 T(x)= [.5 0 ] [x1] horiz.

[0 -.5] [x2]horiz.

# 16 T(x)= [0 1] [x1] horiz.

[1 0] [x2] horiz.

(T of each exercices is just one matrix of two columns and two rows)

#34 Let T: R^n----> R^m be a linear transformation. Show that if T maps two linearly independent vectors onto a linearly dependent set, then the equation T(x)=0 has a notrivial solution.