QUESTION 2 Find vector z that satisfies equation 2u + v - w +32 = 0 with u = (1, 2, 3), v = (2, 2, -1) and w = (4, 0, -4) QUESTION 3 30 points Save Answer Which of the following is true about the following sets? Show why or why not? I- (10 pts.) The set of polynomials of the form ag + 81x + a2x + agx" with ap, a1 , 82 , ag any real numbers and ag not equal to 0, with the standard addition and scalar multiplication operations, is a vector space. Il- (10 pts.) The set ((x, x, x), x is a real number) with the standard addition and scalar multiplication operations, is a vector space. Ill- (10 pts.) The set of all 4 by 4 matrices of the form below, together with the standard addition and scalar multiplication operations, is a vector space. a, b, c, are any real numbers. QUESTION 4 Which of the following is true about the following subsets? Show why or why not? a- (10 pts) The subset of all fifth-degree polynomials or less is a subspace of the vector space of all polynomials. b- (10 pts) The subset of all square lower triangular matrices Lnn is a subspace of Man (the space of all square matrices). c- (10 pts) The subset of all square triangular matrices is a subspace of vector space Man- QUESTION 5 Which of the following is true about the following subsets? Show why or why not? a (10 pts)- The subset W = {(x, y, 3x - 6y); x and y are any real numbers) is a subspace of R3. b- (10 pts) The subset W = {(x, y); x and y are real numbers positive or equal to zero} is a subspace of R3 c- (10 pts) The subset W of R# containing the vectors of the form (x, 0, y, 2) where x and y can be any real number is a subspace of R