• Aucun résultat trouvé

MA 1212: Linear Algebra II Tutorial problems, January 22, 2015

N/A
N/A
Info
Télécharger
Protected

Academic year: 2022

Partager "MA 1212: Linear Algebra II Tutorial problems, January 22, 2015"

Copied!
1
0
0

Chargement.... (Voir le texte intégral maintenant)

Texte intégral

(1)

MA 1212: Linear Algebra II Tutorial problems, January 22, 2015

1.(a) A subspaceUof R4 is the linear span of the vectors

 1 0

−3 1

 ,

 1 4 1 1

 ,

and

 0 2

−5

−1

. Find some basis of this subspace.

(b) A subspaceW of R4 is the linear span of the vectors

−2 2 1 3

 ,

−1

−2

−3

−4

 ,

 0

−3

−1 1

 , and

−3

−6

−4 1

. Find some basis of this subspace.

2.Find some basis for the intersection U∩W of the subspaces from the previous question.

3.Is the subspace spanned by the vectors v1 =

 1

−1 1

 and v2 =

 0 1

−1

 an invariant subspace of the linear transformationϕofR3given by the matrix A=

−4 4 5 16 2 −6

−16 1 9

? Explain your answer.

Références

Télécharger maintenant ( PDF - 1 Page - 53.41 KB )

Documents relatifs

1212: Linear Algebra II Dr. Vladimir Dotsenko (Vlad) Lecture 5

To determine a basis for a linear span of given vectors, the easiest way is to form the matrix whose columns are the given vectors, and find its reduced column echelon form (like

MA 1212: Linear Algebra II Tutorial problems, January 22, 2015

Therefore, this subspace

1212: Linear Algebra II

− a k−1 e k−1 ; this way the condition on linear combinations on the first k vectors of the original basis is automatically satisfied.. The process described in the proof is

1212: Linear Algebra II Dr. Vladimir Dotsenko (Vlad) Lecture 9

(If we introduce a coordinate system corresponding to an orthonormal basis, the vector space gets identified with R n with the usual scalar product, and a symmetric

MA 1212: Linear Algebra II Tutorial problems, February 12, 2015

[r]

MA 1212: Linear Algebra II Tutorial problems, February 12, 2015 1. ∆

[r]

1212: Linear Algebra II

Today we shall start proving the theorems on quadratic forms that you used in the tutorial class last week..

1212: Linear Algebra II

The signature of B is completely determined by eigenvalues of B: the number n + is the number of positive eigenvalues, the number n − is the number of negative eigenvalues, and