Group Solve 1
Math 220
Names: _________________________________________
Write all explanations in complete, correct English sentences.
1. For each matrix below, determine whether its columns form a
linearly independent set. Give reasons for your answers. (Make as
few calculations as possible and do not use rref(.)
 4 12 
A   1  3
  3 8 
7
0
2
B   4  6 5 
 6 13  3
1 5  3 2 
C  0 4  9 18
0 0 0 0 
2. For each matrix in problem 1, determine whether the columns span
R3. Give reasons for your answers. (Make as few calculations as
possible.)
3. Find the standard matrix of the linear transformation T: R2 → R2
that reflects points in the line x2  x1 and then reflects the result in the
horizontal x1 -axis. No explanation is needed if work is shown clearly.
Be careful of the order.
4. Use the inverse of a matrix to solve the following linear system. No
verbal explanation is needed if work is shown clearly.
5 x1  6 x2  1
 7 x1  8 x2  3
5. a. Complete the following definitions using words if possible.
An indexed set v1, v2 ,vn  of vectors is said to be linearly
dependent if …
If A in an m x n matrix, and x is a vector in Rn, then Ax is …
b. Complete the following sentences using the words “always”,
“never” or “sometimes”. You do not need to justify your answer.
It is _____________ possible for six vectors to span R5.
If a linear system has two different solutions, then it
_____________ has infinitely many solutions.
It is _____________ possible to find a matrix that is row
equivalent to infinitely many matrices in reduced row echelon form.