To find a basis for the subspace generated by the given vectors, we need to determine which of the vectors are linearly independent. We can do this by forming a matrix with the given vectors as its columns and performing row reduction to determine if any rows of zeros are produced.
The matrix formed with the given vectors as its columns is:
[1 1 3]
[-4 -3 -8]
[-2 -1 -2]
[1 2 7]
Row reducing this matrix gives:
[1 0 1]
[0 1 2]
[0 0 0]
[0 0 0]
From this row reduced form, we can see that the first and second columns form a basis for the subspace. Therefore, a basis for the subspace is {(1, -4, -2, 1), (1, -3, -1, 2)}, and the dimension of the subspace is 2.
Find a basis and the dimension of the subspace of generated by
{(1, -4, -2, 1), (1, -3, -1, 2), (3, -8, -2, 7)}.
1 answer