Question

Find the dimension of the subspace spanned by the given vectors.

Answer 1

The dimension of the subspace can be found by determining the number of linearly independent vectors that span the subspace.

Step-by-step explanation:

The dimension of a subspace can be found by determining the number of linearly independent vectors that span the subspace. To find the dimension of the subspace spanned by the given vectors, we need to find the number of linearly independent vectors among them.

1. Write the vectors as columns of a matrix.
2. Perform row operations on the matrix to reduce it to row-echelon form.
3. Count the number of pivot columns or the number of leading 1's in the row-echelon form. This will give the dimension of the subspace.

For example, if the row-echelon form has 2 leading 1's, then the dimension of the subspace is 2.