1) Determine whether the following are linear transformations (show that they are, or where they fail...
1) Determine whether the following are linear transformations (show that they are, or where they fail to be and SHOW ALL STEPS in the domain and codomain. ): b) L: P2 →P3 ; L( p(x)) = x2 + p(x)
1) Determine whether the following are linear transformations (show that they are, or where they fail to be and SHOW ALL STEPS in the domain and codomain.): a) L: RR: LX,X2,43)=(x,x) b) L: PP: p(x)) = x² + p(x)
determine weather the following mappings are linear transformations. Either prove that the mapping is a linear transformation to explain why it is not a linear transformation. a)T:R3[x] to R3[x] given by T(p(x))=xp'(x)+1, where f'(x) is a derivative of the polynomial p(x). b) T:R2 to R2 given by T([x y])=[x -y]. Additionally describe this mapping in part b geometrically.
Determine whether the following transformations are linear. A) T(x, y) = (3x, y, y ? x) of R2 ? R3 B) T(x, y) = (x + y, 2y + 5) of R2 ? R2
ui l uentical . i Let A be a square matrix of order n and λ be an eigenvalue of A with geometric multiplicity k, where 1kn. Choose a basis B -(V1, v2,. .. , Vk) of &A) and extend this to a basis B of R". (1) Show that the matrix of the linear transformation x Ax on R" induced by the matrix A with respect the basis B on both the domain and codomain is:
ui l uentical...
For each of the following relations, say which of the properties of reflexivity, symmetry, and transitivity are satisfied and which fail. 13) S on the set, T, of all triangles in the plane defined by t1St2 iff t1 and t2 are similar. 14) R with domain ? and codomain the set, P, of all real polynomials in one unknown m defined by aRp iff a is a root of p. 15) R on the set P X L, where P...
For each of the following transformations: a) Show all Products formed State whether the mechanism favors SN1 or SN2 b) c) Show stereochemistry (*R/S) where applicable. d) Show an arrow that indicates which side of the reaction is favored, products or reactants. Br acetone + NaCN CH3CH2CH2NH2 ш HСІ он
4. For each of the following transformations: a) Show all Products formed b) State whether the mechanism favors SN1 or SN2. c) Show stereochemistry (R/S) where applicable. d) Show an arrow that indicates which side of the reaction is favored, products or reactants. cetone + NaCN CH,CH,CH2NH2 HCI
Determine whether or not the following transformation T :V + W is a linear transformation. If T is not a linear transformation, provide a counter example. If it is, then: (i) find the nullspace N(T) and nullity of T, (ii) find the range R(T) and rank of T, (iii) determine if T is one-to-one, (iv) determine if T is onto. : (a) T: R3 + R2 defined by T(x, y, z) = (2x, y, z) (b) T: R2 + R2...
Find the standard matrix for the following linear transformations from R2 to R2. A contraction in the x direction with factor 1/3. I would greatly appreciate if you show me the steps. Thank you.