# Worksheet: Linear Independence

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

Q1:

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

• ALinearly Dependent
• BLinearly Independent

Q2:

Consider the four vectors

Determine whether they span and whether they are linearly independent.

• AThey span , and they are linearly independent.
• BThey do not 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 is a matrix with a zero determinant, then one column must be a multiple of some other column.

• Afalse
• Btrue

Q4:

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

• ALinearly independent
• BLinearly dependent

Q5:

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

• ALinearly independent
• BLinearly dependent