Worksheet: Linear Independence

In this worksheet, we will practice determining whether a set of vectors is linearly independent.

Q1:

Determine whether the three vectors 123,451,310 are linearly independent or linearly dependent.

  • ALinearly Dependent
  • BLinearly Independent

Q2:

Consider the four vectors 123,433,310,246.

Determine whether they span and whether they are linearly independent.

  • AThey do not span , and they are linearly independent.
  • BThey span , and they are linearly independent.
  • CThey span , and they are linearly dependent.
  • DThey do not span , and they are linearly dependent.

Q3:

Determine whether the following statement is true or false: If 𝐴 is a 3×3 matrix with a zero determinant, then one column must be a multiple of some other column.

  • Afalse
  • Btrue

Q4:

Determine whether the three vectors 120,201,300 are linearly independent or linearly dependent.

  • ALinearly independent
  • BLinearly dependent

Q5:

Determine whether the three vectors 420,221,022 are linearly independent or linearly dependent.

  • ALinearly independent
  • BLinearly dependent

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