Problem
1: Let u=324, v=617, w=052 and z=375.
1. Are the sets cfw_u,v,cfw_u,w,cfw_u,z,cfw_v,w,cfw_v,z and cfw_w,z each linearly independent?
Why or why not?
2. Does the answer to Problem 1 imply that cfw_u,v,w,z is linearly independent?
3. To determine if

Carnegie Mellon University
Department of Mathematical Sciences
21-240 Practice Exam 1, Spring, 2014
Your exam shall consist of problems similar to the homework and quiz
problems.
Monday, February 10th will be a review day. Please ask any questions you
may

Linear Transformation
Recitation 4A
Problem 1: Let b=100 and let A be the
matrix 102314534554. Is b in the range of the linear
transformation xAx? Why or why not?
Solution: Because `b is in the range of the linear transformation xAx is equivalent to
say `

Recitation 1A
Today we covered two examples.
Example 1: Solve the given system of equations.
x14x1+2x22x25x2+x38x39x3=009.
Solution 1: We turn the system into an augmented matrix.
104225189089
Add 4 times the first row to the third row.
1002231813089
Add