MA 1112: Linear Algebra II Tutorial problems, January 29, 2019
Consider two subspaces of R4: the subspace U1 which is the linear span of the vectors
0 3
−2 2
,
−9 8 2
−3
,
4 1 1 1
,
and the subspace U2 which is the linear span of the vectors
6 0
−3 1
,
3 3 0 5
,
9
−1
−5 0
.
1.Find a basis of U1 and a basis of U2. 2.Find a basis for the intersection U1∩U2. 3.Find a basis of U1 relative to U1∩U2. 4.Is the subspace spanned by the vectors v1 =
1
−1 1
and v2 =
0 1
−1
invariant under the linear transformationϕofR3that multiplies every vector by the matrix A=
−4 4 5 16 2 −6
−16 1 9
? Explain your answer.
