Let T₁: R5 R³ and T₂: R³ R² be linear maps.What are the possible dimensions for the kernel of T₂? For each possibilityfind an example.If dim(ker (7₂)) = 3, what is dim(ker(T₂0 T₁))?If T₁ is surjective, what is dim(ker(T₁))?

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Answered: Let T₁: R5 R³ and T₂: R³ R² be linear…

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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Question. 4 Determine the Kernel, nullity and rank of the linear mapping T:R³ R³ as follow. y T(=) = x-2y y-3t t-4s
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Let A(0,-2), B(0,4) (1) Find the set of all points P(x, y) such that m(PA)=2 m(PB) (2) Convert the equation in standard form and fully identify the equation.
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8. Decide which of the following sets are linearly independent in R. Justify your answer in each case. (a) X₁ = {(1,0), (0, 1)} CR² (b) X₂ = {(1,0), (2,0)} CR² (c) X3 = {(-1,0), (0,0)} CR² (d) X₁ = {(1,0), (0, 1), (1, 1)} CR² (e) X5 = {(1,0,0), (0, 1, 0), (1, 1, 1)} CR³ (f) X6 = {(1,0,0), (0, 1, 0), (1, 1, 1), (-1,0,1)} CR³ (g) X7 = {(0, 0, 0), (0, 1, 0), (1, 1, 1), (-1,0,1)} CR³ (h) Xs = {(0, 1, 0), (1,1,1)} CR³ (i) X9 = {(4,3,0,0), (0, 0, 1, 1), (0, 0, 0, 1), (1, 0, 0, 1), (0, 1, 0, 1)} CR¹ (j) X10 = {(1,2,0,0), (0, 2, 3,0), (0, 0, -1, 1)} CR¹
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Let T₁: R5 R³ and T₂: R³ R² be linear maps. What are the possible dimensions for the kernel of T₂? For each possibility find an example. If dim (ker (7₂)) = 3, what is dim (ker(T₂0 T₁))? If T₁ is surjective, what is dim (ker(T₁))?