Worksheet: Basis and Dimension of a Given Span

In this worksheet, we will practice checking the linear dependence of given vectors to find a basis and the dimension of their span.

Q1:

Determine a basis and the dimension of the given span.

  • Abasis , dimension
  • Bbasis , dimension
  • Cbasis , dimension
  • Dbasis , dimension
  • Ebasis , dimension

Q2:

Determine a basis and the dimension of the given span

  • A basis , dimension
  • B basis , dimension
  • C basis , dimension
  • D basis , dimension
  • E basis , dimension

Q3:

Determine a basis and the dimension of the given span.

  • A basis , dimension
  • B basis , dimension
  • C basis , dimension
  • D basis , dimension
  • E basis , dimension

Q4:

Determine whether the given three vectors are linearly independent or linearly dependent.

  • Alinearly independent
  • Blinearly dependent

Q5:

Determine whether the three given vectors are linearly independent or linearly dependent.

  • Alinearly independent
  • Blinearly dependent

Q6:

True or False: Any set of 4 vectors in a 3-dimensional vector space must be linearly dependent.

  • ATrue
  • BFalse

Q7:

Determine whether the three given vectors are linearly independent or linearly dependent.

  • Alinearly dependent
  • Blinearly independent

Q8:

Fill in the blank. The of 𝑚 orthogonal vectors is 𝑚 -dimensional.

  • Akernel
  • Bcollection
  • Ctransformation
  • Dspan

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.