Question

Find the dimension of the subspace spanned by the given vectors. [Start 3 By 1 Matrix 1st Row 1st Column 1 2nd Row 1st Column negative 2 3rd Row 1st Column 0 EndMatrix ]1 −2 0 ​, [Start 3 By 1 Matrix 1st Row 1st Column negative 1 2nd Row 1st Column 3 3rd Row 1st Column 1 EndMatrix ]−1 3 1 ​, [Start 3 By 1 Matrix 1st Row 1st Column 2 2nd Row 1st Column 1 3rd Row 1st Column 5 EndMatrix ]2 1 5 ​, [Start 3 By 1 Matrix 1st Row 1st Column negative 1 2nd Row 1st Column 1 3rd Row 1st Column 1 EndMatrix ]−1 1 1 The dimension of the subspace spanned by the given vectors is nothing

Answer 1

Answer:

4

Step-by-step explanation:

Given the following column vectors

(1, -2, 0), (-1, 3, 1), (2, 1, 5) and (-1, 1, 1)

Before we can get the dimension of the vector, the following steps must be followed;

Step 1:

We need to transform the vectors given into a matrix form and then reduce the resulting matrix.

Step 2:

Then we generated the basis of the matrix (new set of column vectors from the reduced matrix).

Step3:

The total number of column vectors generated will be equivalent to the dimension of the vectors.

The dimension spanned by the set of vectors is 4

Check the attachment for calculation