Answer:
The vectors does not span R3 and only span a subspace of R3 which satisfies x+13y-3z=0
Explanation:
The vectors are given as
Now if the vectors would span the , the rank of the consolidated matrix will be 3 if it is not 3 this indicates that the vectors does not span the
.
So the matrix is given as
In order to calculate the rank, the matrix is reduced to the Row Echelon form as
As the Rank is given as number of non-zero rows in the Row echelon form which are 2 so the rank is 2.
Thus this indicates that the vectors does not span
<em>Now for any vector the corresponding equation is formulated by using the combined matrix which is given as for any arbitrary vector and the coordinate as </em>
<em /><em />
<em /><em />
<em /><em />
<em /><em />
<em /><em />
Now converting the combined matrix as
From this it is seen that whatever the values of the coordinates does not effect the value of the plane with equation as
So it is verified that the subspace of R3 such that it satisfies x+13y-3z=0 consists of all vectors.
<em />