# 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?

- Rank minimum of .
- Column space is a subspace of .
- Dimension of column space dimension of row space.
- 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