Are the following sets vector spaces? Give reasons. 2. a) pe P4 p(1) 0 and p(-1)...
1. For each of the following vector spaces, give two differ- ent spanning sets: (b) M22 (c) P2 (a) R
2) Determine if each of the sets below is a vector space, give a basis if it is a vector space or an explanation if it is not a vector space. Зр 2q -P p +9) p.q ER {[1]: a+c=0} ; T,S, ER 2t
1. Why the following sets are not vector space? with the regular vector addition and scalar multiplication. a) V = {E: * > 0, y 20 with the regula b) V = {l*: *y 2 o} with the regular vector addition and scalar multiplication. c) V = {]: x2+y's 1} with the regular vector addition and scalar multiplication. 2. The set B = {1,1+t, t + t2 is a basis for P, the set of all polynomials with degree less...
(1 point) Find a basis for the column space of 0 A = -1 2 3 3 - 1 2 0 - 1 -4 0 2 Basis = (1 point) Find the dimensions of the following vector spaces. (a) The vector space RS 25x4 (b) The vector space R? (c) The vector space of 6 x 6 matrices with trace 0 (d) The vector space of all diagonal 6 x 6 matrices (e) The vector space P3[x] of polynomials with...
vi) Consider the following polynomials in the vector space of polynomials of degree 3 or less, P3. Pi(x) 12 +3r2 +a3 P2(x) 132 Pa(r) 1242 P4(z) = 1-r + 3r2 + 2r3 Which of the following statements are true and which are false? Explain your answer. a) The set {Pi, P2,P3} is a basis for P3. b) The set {Pi,P2, p3,P4,P5} İs a linearly independent set in P3. vi) Consider the following polynomials in the vector space of polynomials of...
Math 407 Homework 4 Name: 1. Why the following sets are not vector space? with the regular vector addition and scalar multiplication. b) v = {(7: «y 20} with the regular vector addition and scalar multiplication. with the regular vector addition and scalar multiplication. 2. The set B = {1,1+t, t+t?} is a basis for P, the set of all polynomials with degree less than or equal to 2. Find the coordinate vector of p(t)-5+21+342 3. Let H =Span{ői, üz.us)...
1. (15 points) Prove whether the following sets are linearly dependent or independent, and determine whether they form a basis of the vector space to which they belong. s 10110 -1 ) / -1 2) / 2 1 17 ) } in M2x2(R). "11-21 )'(1 1)'( 10 )'(2 –2 )S (b) {23 – X, 2x2 +4, -2x3 + 3x2 + 2x +6} in P3(R) (the set of polynomials of degree less than 3. (c) {æ4—23+5x2–8x+6, – x4+x2–5x2 +5x-3, x4+3x2 –...
1. Which of the following sets are linear spaces? a) {X = (21, 22, 23) in R’ with the property 11 – - 2x3 =0} b) The set of solutions of Az = 0, where A is an mxn matrix. c) The set of 2 x 2 matrices A with det(A) = 0. d) The set of polynomials p(x) with S-, p(x) dx = 0. e) The set of solutions y = y(t) of y' + 4y' +y = 0.
6. For the following vector spaces V, determine if the subset H is a subspace. If not, give one reason why H fails to be a subspace. (a) (5 points) V is the set of functions f from R + R, and H is the set of polynomials of integer coefficients. (b) (5 points) V = P, is the vector space of polynomials of degree at most 2, and H is the subset of all polynomials in P2 of the...
Price, Cost 3 P D P4 4 P3 3 C P2 2 B Р. 2 0 21 Q2 Quantity If a positive externality exists then market equilibrium price is P3 P4 OP1 OP2