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.
What is the row space of matrix of size a subspace of?
- B and
Consider the matrix of size .
Dimension of the row space of .
- Arank of
- Cdeterminant of
- Dtrace of
The column space of matrix of size is a subspace of .
- C and
The column space of .
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
What is the dimension of the row space of the matrix
Find the basis for the column space of the matrix
Find the basis for the row space of the following matrix: