Mark44 said:The question you're trying to answer is whether y = c1*(column 1 of A) + c2*(column 2 of A) + c3*(column 3 of A) for some scalars c1, c2, and c3. Set up an augmented matrix with this information and use row reduction (I believ this is also called Gaussian elimination) to find out.
To determine the span of a subspace in R^4, you can use the given vectors (6,7,1,s) and set up a system of equations. You will need to solve for the values of 's' that satisfy the system of equations. The span of the subspace will be all possible linear combinations of the given vectors.
No, you cannot use any vector in R^4 to span the subspace. The given vectors (6,7,1,s) must be linearly independent in order to span the subspace. This means that none of the vectors can be written as a linear combination of the others.
To determine if the given vectors span the entire R^4 space, you can check if the dimension of the subspace is equal to the dimension of R^4. In this case, since there are four vectors in R^4, the dimension of the subspace will need to be four in order to span the entire space.
Yes, there are other methods that can be used to solve subspace spanning homework in R^4. For example, you can use the Gram-Schmidt process to obtain an orthonormal basis for the subspace, or you can use row reduction to find the basis for the subspace.
No, there is no specific order in which you need to arrange the given vectors. As long as the vectors are linearly independent and span the subspace, the order in which they are arranged does not matter.