May I please ask someone please help me write the detail solution with these questions, many thanks.

(1) Suppose that U and W are both 5 dimensional subspaces of R9. Show that UnW / {}. (2) Suppose that V = U1 + U2 + . . . + Un, where each U is a subspace of V. Prove V = U1 0 U2 0 . .. Un if and only if the sum of the dimensions of the Ui equals the dimension of V. (3) Suppose V is a finite-dimensional vector space and R, S, T : V - V are linear maps such that RST is surjective. Show that S is injective. (4) Let p be a polynomial. Show that there exists a polynomial q such that 6q" - 29" + 29 = p. Here q'" denotes the third derivative of q, q" denotes the second derivative, and q' denotes the first derivative. Recall from the text that the degree of the 0 polynomial is -co. Use linear algebra, not calculus, to solve this