 
Summary: 18.024ESG Exam 1
Pramod N. Achar
Spring 2000
1. Below are listed several linear subspaces of Rn
, each with a set of vectors. For each set of vectors,
decide whether it is linearly independent, and decide whether it spans the given subspace. Finally, find
the dimension of the subspace. Answers alone will suffice; you do not need to give any justification.
Linearly Spanning
Linear subspace Vectors independent? set? Dimension
{(x1, x2, x3)  x1 + x2 + x3 = 0} R3 (1, 1, 0)
(0, 1, 1)
{(x1, x1, x1)} R3 (1, 1, 1)
(1, 1, 1)
R4
(1, 1, 0, 0)
(0, 1, 1, 0)
(0, 0, 1, 1)
2. Solve the following system of equations by GaussJordan elimination.
x + y + 3z = 5
2x  y + 4z = 11
