7. V={[)a620) a vector space! Draw the vector space? Draw the graph and explain why or...
Let V = R3 be a vector space and let H be a subset of V defined as H = {(a, b,c) : a? = b2 = c}, then H Select one: O A. satisfies only first condition of subspace B. is a subspace of R3 C. None of them O D. satisfies second and third condition of subspace
Why does this show that H is a subspace of R3? O A. The vector v spans both H and R3, making H a subspace of R3. OB. The span of any subset of R3 is equal to R3, which makes it a vector space. OC. It shows that H is closed under scalar multiplication, which is all that is required for a subset to be a vector space. OD. For any set of vectors in R3, the span of...
Problem 1. Given the vector space Pa, the basis B =< 1,7,22,,24 > of Pd, let U = span[1, 2], V = span[22, 1) and W = span[r2,, ). Which of the following statements is true? 1. UmV = 0 2. UUV is a vector subspace of P. 3. U W = 0 and for any vector subspace P of PA, U, W CP 4. UUW =P 5. All except statement 3 is false. P =P.
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) Determine whether the given set S is a subspace of the vector space V. A. V = R", and S is the set of solutions to the homogeneous linear system Ax = 0 where A is a fixed mxn matrix. B. V is the vector space of all real-valued functions defined on the interval (-oo, oo), and S is the subset of V consisting of those functions satisfying f(0) 0 C. V Mn (R), and S is the...
linear algebra help 4a. Let It be a non empty subset of a vector space Y, Write the 3 properties for H to be o subspace of y. show that H= 18 9,6 ER a subspace of R4 show that span { v. 7,33} is a subspace of v + 7V2, V E Ve showthat the vegtos (3109) sporno
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...
Problem 1. Given the vector space P the basis B -<1,7,',r'> of P, let U - span[1,2]. V-span c and W -spanr x '] Which of the following statements is true? 1. UV = 0 2. UUV is a vector subspace of P -P 3. U nW - and for any vector subspace P of P UW SPP 4. UUW = P. 5. All except statement 3 is false. Problem 2. Consider the function P, R such that f(1-r) -...
Problem 6. Let V be a vector space (a) Let (--) : V x V --> R be an inner product. Prove that (-, -) is a bilinear form on V. (b) Let B = (1, ... ,T,) be a basis of V. Prove that there exists a unique inner product on V making Borthonormal. (c) Let (V) be the set of all inner products on V. By part (a), J(V) C B(V). Is J(V) a vector subspace of B(V)?...
6. (a) Let V be a vector space over the scalars F, and let B = (01.62, ..., On) CV be a basis of V. For v € V, state the definition of the coordinate vector [v]s of v with respect to the basis B. [2 marks] (b) Let V = R$[x] = {ao + a11 + a222 + a3r | 20, 41, 42, 43 € R} the vector space of real polynomials of degree at most three. Write down...