Consider the groups (R,+) and (R x R. +). Define the map Rx (RX R) → Rx R defined by ra (z. y) = (x+ry.y). Show that this map is a group action. (b). Find Orb((1, 0)), Orb ((1, 1)) and Stab((0,0)).

Q: 1. True or False. (a) R³ is isomorphic to R³*2. (b) p19 is isomorphic to R4x5 (e) Span (1+x, x-²,…

A:

Q: Let T : P2 → P, be the linear transformation defined by T(ax? + bx + c) d -(ax² + bx + c). dx T(3x?…

A: Topic - linear transformation

Q: Let 7: R→ R be a linear transformation such that 7(1, 1, 1) = (4, 0, -1), 7(0, -1, 2) = (-5, 5, -1),…

A:

Q: Let T : R² R2 be a linear transformation such that T(x₁, x₂) Find x = (1, 2) such that T(x)…

A:

Q: 8. Let T₁ R2 → P₁ (R) and T₂: P₁ (R)→ R2 be the linear transformations given by: (a₁ + a²) + (a₁ −…

A:

Q: 2.3: We have showed that (aa CIR),.) is a group in our lectures Show that the map det: GL, CIR)→…

A: p

Q: Let ū -- and = T(u) T(v) Define the linear transformation T: R³ → R² by T(x) = A. Find the images of…

A:

Q: 11. Explain whether there exists a linear transformation T:R. → R2 such that T(0, 1, 1, 1) = (2,0),…

A: A transformation is called linearly independent when the nullity of the transformation is 0.…

Q: Let x= then find the transformation R (x). 33-2 2. -3-23 2 None of these 3/3-2 -3-33 3-23 2 -2-33

A:

Q: 4. Consider the the linear maps f: R² R² and g: R² R² given by f((x, y)) = (x-y,2+ y) and g((x, y))=…

A:

Q: Let T :U → V be a linear transformation. Use the rank-nullity theorem to complete the information in…

A: The given table is - We know that dim(U) = dim ℝm×n = m×n For ℝ1×2 dim (U) = 2 Using rank nullity…

Q: The matrix A = " 1 0 0 2 # is a linear map from R 2 to R 2 . Draw the modified shape of the circle x…

A: The matrix A=1002 is a linear map from ℝ2 to ℝ2 . To Draw: The modified shape of the circle x2+y2=1…

Q: 21. Let T R² T(x1, x₂) T(x) = R2 be a linear transformation such that (x₁ + x2, 4x₁ + 5x2). Find x…

A: Please check the answer in the next step. This is very straight forward.

Q: 3) Given the mapping T: R² → R³ defined by T(x1 , X2) = (3x1 – 2.x2, 4.xj + 5x2, x1 –x2) a) Prove…

A:

Q: Define a linear transformation T : P, → R² by T(p : p(-1) + p(2) p(3) (a) Find the kernel space of…

A:

Q: Let a = (0, 3, 5) and 6 = (0, 1, 4). Find the projection of b onto a. proja b V - λ

A: Given:        a→=0,3,-5         b→=0,1,4 The projection of b→ onto a→ is:…

Q: 4. Consider the map T : P1 → R² given by T(a+bt) – Show that T is a lincar transformation. Determine…

A:

Q: 8. Show that the mapping T: V,(R) → V½(R) defined = (3a, - 2az + az3, a1 – 3a, – 2az3) is a linear…

A:

Q: Which of the following mappings on E2 is not a transformation? Choose the correct answer I.…

A: E2 is of the form (0, x) type, that is second component is non zero.  Therefore option second is not…

Q: Let f(z) = (az + b)/(cz + d) and ad – bc # 0. If this transformation maps zo → Wo, 1→ W1 and Z2 → W2…

A: Given , f(z)=(az+b)(cz+d) , ad-bc≠0.  This transformation maps z0→w0, z1→w1 and z2→w2 Taking…

Q: 2. Suppose that G is a lincar map such that G(2,0) = (4, 0) and G(0, 3) = (–3, 9). Find the images…

A: Given that, G(2, 0) = (4, 0) G(0, 3) = (-3, 9) G is a linear map. Then we get, (a) G(1, 0) = (2, 0)…

Q: The linear transformation T: R³ → R² is defined by T(x)= Ax, where 0-27 A 10 0 11 Find ker(7).…

A:

Q: T (x, y) (2x,y) is an is %3D

A: T(x,y)=(2x,12y) The transformation of any figure changes the size, shape and the position to create…

Q: Let →a=⟨−4,1,−2⟩a→=⟨-4,1,-2⟩ and →b=⟨−2,−3,4⟩b→=⟨-2,-3,4⟩. Find the projection of →bb→ onto →aa→.…

A: