# Worksheet: Row Space and Column Space

In this worksheet, we will practice defining the row and column spaces of a matrix and finding the basis and dimensions of these vector spaces.

Q1:

What is the row space of matrix of size a subspace of?

• A
• B and
• C

Q2:

Consider the matrix of size .

Dimension of the row space of .

• Arank of
• B
• Cdeterminant of
• Dtrace of
• E

Q3:

The column space of matrix of size is a subspace of .

• A
• B
• C and

Q4:

The column space of .

• A
• B
• C
• D

Q5:

For matrix of size , which of the following statements is true?

1. Rank minimum of .
2. Column space is a subspace of .
3. Dimension of column space dimension of row space.
4. Row space is a subspace of .
• AII only
• BI, II, and III
• CI, III, and IV
• DII and III
• EIII and IV

Q6:

What is the dimension of the row space of the matrix

Q7:

Find the basis for the column space of the matrix

• A
• B
• C
• D
• E

Q8:

Find the basis for the row space of the following matrix:

• A
• B
• C
• D
• E