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...
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)
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: R →R; L(x,x,x)=(x,x;) b) L: P, P; L(p(x)) = x + p(x)
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...
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.
6. (16 points) For the two linear transformations defined as T: Pz → P3, T1(p) = xp' T2 :P3 → P1, T2(p) = 3p". a) Determine whether Ti is an isomorphism? (Clearly show your work and explain.) b) Show how to find the image of p(x) = 3 - 4x + 2x² – 5x’ through the T2 transformation. c) Show how to find the standard matrix for the linear transformation that is T =T, •T,. d) Show how to find...
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
4. Determine whether the polynomials Pi = 1 + x, P2 = 1 + x2, P3 = x + 2 are linearly independent or linearly dipendent in P3.
please write neatly and show all steps. thank you
unena11Ic.doc 10. Determine whether the given collection is linearly independent in P3. A) x3-x, x2- 1, x, 1) B) 1, 1+x, x + x2, x2+ x}e8onil A C) {x3 +x2+x+ 1, x3 + x2 + x, x3 + x2, x3) D) {x3 +x2 +x +1, x+x, x +1}woor aan 11. Determine whether the given collection is a spanning set of R. A) <0, 1, 1>, <1, 0, 1>, <1, 1, 0>}...
linear algebra
3. Determine whether the function (p,q)= a, b + ab + ab, where p(x) = 4, + ax + ax and g(x)=bo bat checking the following axioms of the definition of an inner product: 40 72x+ax and g(x)=b, +bx+b.rbelong to P2 represents an inner produd A) (5,8)=(8,8) B) (f, g+h)=(5,8)+(f,h) C) c(f,)=(cf,8) for any scalar c D) (f, f)20, and (f, f)=0 if and only if f(x)=0
Q22 A` = AP, B` = BQ
5.4 Composition of Linear Transformations229 Let T be the linear transformation from P3 over R to R2x2 defined by ao T (ao+ ax azx a3x) ao t a3 a3 Find bases A' of Pa and B' of R22 that satisfy the conditions given in Theorem 5.19. 23. Let T be the linear transformation from R2x2 to P2 0ver R defined by a12 a22 +(a1-a22)x +(a12 -a21)x T a22 Find bases A' of R2x2...