Prove/Disprove that HUK is a subspace of V.Prove that if V, W are vectors spaces, ...., VV are linearly independent, and T:V → W is alinear 1-1 transformation then T(y),...,T(v.) are also linearly independent. (Explain why the 1-1-ness is crucial)Given the vectors22498 -18determine the dimension of the subspace spanned by

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Answered: Prove/Disprove that HUK is a subspace…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Please solve the chapter about linear algebra fast max 60 minutes thank u
Let V be a vector space, and TV →Va linear transformation such that T(271 +372) = -201 +502 and T(371 +50₂) = 371 - 572. Then T(v₁) =₁+₂, T(₂)=₁+₂, 40₂) = ₁+ T(471
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Let M₂x2 be the vector space of all 2 x 2 matrices and define a linear transformation T: M2x2 → M2x2 by a [id] Describe the kernel of T. C T(A) = A + AT, where A = O No answer text provided. odlo 0 -a ° 0 O [1] :d is a real number} [9] : b is a real number} -b O (1 :d is a real number} (d c is a real number} °41 :d is a real number} : a,b,c,d are real numbers} [9] : b is a real number}
Let fi = 1+2x + 3x², f2 = 2 + 3x + 4x². B = (f1, f2) is a basis for the subspace V = {ao +a1x+azx²[ao – 2a1 +a2 = 0} of R2[r]. Let g = 1+5x + 9x². If [g]g = (,) then s = a) -7 b) -5 c) 5 d) 7 e) g is not in V.
Q1) Let S (x-3, x² + 2x, x² + 1). Is S is span (P2(x)) or not? Q2) Let T= ((2,-2,4), (3,-5,4), (0,1,1)). Show that whether T is linearly independent or not? Q3) Let N = (vv) be a basis for vector space V Show that every vector in V can be written as uniquely linear combination of vectors of V.
4. Let V and W be finite dimensional vector spaces. Let T : V –→ W be a linear transformation of V into W. (a) Let H be a subspace of V. Let T(H) be the set of all images of the vectors in H under the transformation T. Show that T(H) is a subspace of W and dim T(H) < dim H (b) Now suppose that T is one-to-one. Show that dim T(H)= dim H.
P3 = {ao + a¡t + azt² + a3t³ : ao, a1, az E R} be the vector space consisting of all polynomials of degree less than or equal to 3. Observ basis for P3, where B = {1, t, t², t³}. Let T : P3 - P3 be a linear transformation defined by T(ao + ajt + azt² + a3t°) = a1 + 2a2 + 6azt Find the matrix representation [T]B_of T with respect to B.
-(.. Suppose that T: V V is a linear transformation and V is a finite dimensional vector space. Suppose that U is a subspace of V such that T(U) = T(V). Prove that U + ker(T) = V. %3D
4) Please correctly and detailed justification are required

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Prove/Disprove that HUK is a subspace of V. Prove that if V, W are vectors spaces, V,...,V, V are linearly independent, and T:V →W is a linear 1-1 transformation then 7 (v.),...,T (v) are also linearly independent. (Explain why the 1-1- ness is crucial)