Linear Algebra Quiz 1
Name:
Surname:
Group:
1. Given vectors u1= (1,2,3), u2= (2,3,7), and u3= (3,5,6) in R3, express the
vector w= (7,13,10) as a linear combination of u1, u2, u3.
2. If a linear transformation T:Rn→Rmmaps Rnonto Rm, can you give a relation
between mand n? If Tis one-to-one, what can you say about mand n?
3. Determine whether the following four vectors in R4are linearly independent or
dependent:u1= (1,0,2,−1), u2= (3,−1,0,4), u3= (0,2,−3,1), u4= (2,1,1,0)
4. Compute the matrix product E F , where E=
1 2 0
−1 3 1
4 0 2
, F =
0−2 1
310
124
.
5. Find the inverse of the following matrix (if it exists): B=
2 0 1
1 1 0
3 2 1
1