a) Find a linearly independent set of vectors that spans the same subspace of R^3 as that spanned by the vectors
Vector u = [[-3],[-3],]
Vector v [[-1],[-1],[-3]]
Vector w = [,,]
b) Write vector w as a linear combination of vector u and vector v .
Find the a basis for the set of vectors.So form a matrix, with each row being formed by a vector.
Reduce it to row echelon form ( May be by Gaussian elimination) as.
This means that only two of the vectors in set are linearly independent i.e. u and v vectors alone will span the same subspace of R^3 as all three vectors.
solving this sytem we get a=b=(-1/2)