5 154Let T be a linear transformation from R³ to R² such that [T]/(0,2,3)} is a base of R³ and C is the canonical base of R² respectively.c) Calculate a basis for the image of T=2), where B = {(1,0,0), (0,1,1),9

Given is a linear transformation T from ℝ3 to ℝ2 such that TBC=512549 Also given B=1,0,0, 0,1,1,…

Answered: transformation from R³ to R² such that…

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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Let the vectors (i, j, k) constitute an orthonormal basis. In terms of this basis, a general basis is: e₁ = 71 + 5ĵ + 5k, e₂ = 7î + 5j + 2k, e3 = 2î + 2) + 7k. Determine the dual basis (e¹, e², e³) of the above general basis in terms of (î, j, k). For vector A = 21 + 7ĵ + 5k, determine its contra-gradient components (A¹, A², A³) and co-gradient components (A1, A2, A3).
{[i :]:[ 1 0 0 0 ; :]:[: :)-[: :]} 1 1 1 0 1 1 - Let B a basis for M2(R). = 0 0 1 1 Find the coordinate vector [A]B_ relative to the basis B, where a b (a) A (а) А — с d -1 3 (b) А — 2 5
Let X = 0 2 -2 1 and A = 3 0 0 3 0 3 0 -2 -2 0 0 -4 -4 0 1 -4 -1 0 1 0 1 0 0 (a) Find a basis for Nul(A). (b) Find the projection of × on to Nul(A). Call this vector ĂNul. (c) Find a basis for Row (A). (d) Find the projection of x on to Row(A). Call this vector XRow. (e) Show that XNul and Row are orthogonal. Will this be the case for all matrices A and all vectors x? Explain.
Let 3 -4 3 0 3 -4 2 -3 3 1 A: 7 -8 6 0 6 11 - -10 9 - -3 5 A basis for the column space of A is { vector
Show that B = {(1,1,1), (1,–1,0), (1,1, –2)} is an orthogonal basis of R³ and then expand x = (a, b, c) as a linear combination of the basis vectors using the Fourier Expansion Theorem.
Let A = [v v vi = (1,0,0,0) V2 = (1,2,0,0) vs = (1,1,0, 0) vA = (2,1, 1,0) v = (0,1, 1,0) v v5 where %3D V5 Which vectors form a basis for the column space? And how many vectors are there in the basis of the null space? O v 3 O 2 vectors in basis null space O 3 vectors in basis of null space O v 1 O v_4 O v 2 O v_5 O 4 vectors in basis of null space O 1 vector in basis of null space
Apply tion process the Gram-Schmidt orthonormaliza- to transform the basis B = for R with {(1, 1,0, 1), (1, –2,0,0), (1,0, –1, 2)} standard inner product into an orthonormal basis.
Exercise 4.3 Find all the vectors of R³ which have the same coordinates in the canonical basis and in the basis = {(5, 18, 22), (-1,-8,-1), (1,-1, 12)}.
Answer pls
Let V=R? and let (R²)* be the dual space for R?. Find the basis {o1, 02} that is dual to the following basis of R?: {vi=(2, -2.), v2=(0, 2 )}. Find the basis {V1, V2} of R? that is dual to the basis {01, 02} of (R?)* defined by d1(x, y)=2 x+2y; 02(x, y)=2x;

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transformation from R³ to R² such that [7] = (5 3), where B = {(1,0,0), (0,1,1), 5 1 5 4 Let T be a linear (0,2,3)} is a base of R³ and C is the canonical base of R² respectively. c) Calculate a basis for the image of T