only need q4 solution.. please provide justified solutions as soon as possible to get upvote..

Math335 Linear Algebra One a Day 13 Linear Vector Spaces: Linear Independence, Basis, and Dimension Consider the set S of polynomials given below: (2x* + 2x3 -7x2 -5x-6. 3x* +3x3+7x2-5x-12 , 5x* +5x' -10x -18. S=x+x+14x -6. 4x* + 4x3 -14x3-10x-6 , 7x* +7x3 -7x3 -15x-18 , 10x* +10x - 20x-36 1. Determine which vectors in S can be written as linear combinations of other vectors in the set and write down the specific relationships. 2. Write down a basis set which spans the same subspace as set S. 3. What is the dimension of this basis? 4. By now you have discovered that the vectors in set S are unable to space all polynomials of degree 4 or less. Suppose someone gives you an additional set of vectors T, given below: (x*+x+x+x-6, -x* -x3 +21x* +5x , T= 2x* +2x3 -12x+11, x+1, -5x2 -13x +8 Expand your basis set in part 2 above by selecting any vectors you need (and only the ones you need) from set T. What is the dimension of your new, expanded basis