29. Let T be linear transformation from a vector space U (F) into a vector space r)and a, a2, ..., C, ethen show that a,, a2,E U. If T(a), T (a), . . , T (a,) are linearly independent..., An are linearly independent.

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Answered: Let T be linear transformation from a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Let V be a vector space and T: V->V be a linear map such that T^2=T. 1) Prove that lm(T)=ker(Id-T) 2) Prove that V=ker(T)⊕Im(T)
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Plz do both subparts
Let V be the vector space of functions spanned by B = {bị 2 sin r + 6 cos a, b2 = 3 sin a + 7 cos a} where a + %3D C = {ci = sin a, c2 = of coordinates matrix P ne Z is also a basis for V. Find the change 2 = cos a} where a + C+B Ex: 5 P = C-B The coordinates of a function f(x) relative to the basis B are [f(x)]B Find the coordinates of f(æ) relative to Cand find f(æ). Ex: 5 [f(x)]c = f(x) = Ex: 5 sin z + cos a
Let U,V ,W be finite-dimensional F-vector spaces and let T:U → V, S:V→W be linear transformations. Prove that nullity(S • T) - nullity(T ) = dim(im(T ) N ker(S)) following steps (a)-(c) below. a) LetU:=ker(S-T)andT:=T|u.Prove:im(T').=T(U')=im(T)N ker(S ). b) Prove:ker(T')=ker(T). c) Deduce:nullity(S•T)-nullity(T)=dim(im(T)nker(S)).
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Consider the following hypothesis test. Ho: H1 - H2 = 0 Ha: H1 - 42 # 0 The following results are from independent samples taken from two populations assuming the variances are unequal. Sample 1 Sample 2 n1 35 = 40 = 13.6 X, = 10.1 S1 5.8 S2 = 8.1 (a) What is the value of the test statistic? (Use x, - x2. Round your answer to three decimal places.) (b) What is the degrees of freedom for the t distribution? (Round your answer down to the nearest integer.) (c) What is the p-value? (Round your answer to four decimal places.) p-value = (d) At a = 0.05, what is your conclusion? Do not Reject Ho: There is sufficient evidence to conclude that u, - µ, ± 0. Reject Ho. There is sufficient evidence to conclude that µ, - µ, # 0. Do not Reject Ho. There is insufficient evidence to conclude that u, - H, + 0. 0' Reject Ho. There is insufficient evidence to conclude that u1 - µ2 ± 0.

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Let T be linear transformation from a vector space U (F) into a vector space nr) and a, a2, then show that a,, az, ..., a, are linearly independent. , Cm E U. If T(a), T (a,), . . , T'(a,) are linearly independent ... ....