MAT2611 Assignment 03 Solutions 2026
UNISA
Due Date: 29 June 2026
All the questions are fully solved completely, all steps and calculations are shown
, Problem 1
Find a basis for the subspace of ℝ5 spanned by
𝑣1 = (1,3,1,2,1)
𝑣2 = (0,1,3,2,1)
𝑣3 = (1,0,1,0,1)
𝑣4 = (0,2,0,1,1)
Form a matrix using the vectors as columns
1 0 1 0
3 1 0 2
𝐴= 1 3 1 0
2 2 0 1
[1 1 1 1]
Perform row reduction.
The reduced row echelon form is
1 0 0 0
0 1 0 0
RREF(𝐴) = 0 0 1 0
0 0 0 1
[0 0 0 0]
: Identify pivot columns
Pivot columns are:
1, 2, 3, 4
Therefore all four vectors are linearly independent.
Basis
1 0 1 0
3 1 0 2
1 , 3 , 1 , 0
2 2 0 1
{(1) (1) (1) (1)}
Answer
A basis for the subspace is
{𝑣1 , 𝑣2 , 𝑣3 , 𝑣4 }
Dimension: dim(𝑊) = 4
UNISA
Due Date: 29 June 2026
All the questions are fully solved completely, all steps and calculations are shown
, Problem 1
Find a basis for the subspace of ℝ5 spanned by
𝑣1 = (1,3,1,2,1)
𝑣2 = (0,1,3,2,1)
𝑣3 = (1,0,1,0,1)
𝑣4 = (0,2,0,1,1)
Form a matrix using the vectors as columns
1 0 1 0
3 1 0 2
𝐴= 1 3 1 0
2 2 0 1
[1 1 1 1]
Perform row reduction.
The reduced row echelon form is
1 0 0 0
0 1 0 0
RREF(𝐴) = 0 0 1 0
0 0 0 1
[0 0 0 0]
: Identify pivot columns
Pivot columns are:
1, 2, 3, 4
Therefore all four vectors are linearly independent.
Basis
1 0 1 0
3 1 0 2
1 , 3 , 1 , 0
2 2 0 1
{(1) (1) (1) (1)}
Answer
A basis for the subspace is
{𝑣1 , 𝑣2 , 𝑣3 , 𝑣4 }
Dimension: dim(𝑊) = 4
