6 Let b₁ =[2] b₂ =[4]3 JCI13V=V-29²₁-[2] 2² =²²] =1²-2and consider the bases forR²bzgiven by B = { b₁,b₂}andC = {0₁₂ (₂3Finda)b) [V] b;part a)c) [V]c using the results froma) and b)the change-of-coordinates matrixfrom B to C

Answered: Image /qna-images/answer/6b4c5462-fe02-4ec7-9a10-5607a3f25ef1.jpg

Answered: 6 Let b₁=[2] b₂ = 3 4 [ C₁ = [ ² ] ² ₂…

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 B= (b,.b2} and C = (c1,c2} be bases for a vector space V, and suppose b, = 3c, - 7c2 and b2 = 5c, - 6c2. a. Find the change-of-coordinates matrix from B to C. b. Find [x]c for x= 4b, - 5b2. Use part (a). а. Р C-B b. [x]c (Simplify your answer.)
2 Consider the matrix A = and the vector u = Let B = (A – A")2 and define vector v = Bu. If v = , write 1 down the value of vị. [Please enter your answer numerically in decimal format.
Let B = {b₁,b₂} and C= {C₁,C₂} be bases for a vector space V, and suppose b₁ = -6c₁ +9c₂ and b₂ = 7c₁ - 5c₂. a. Find the change-of-coordinates matrix from B to C. b. Find [x]c for x = 7b₁-3b₂. Use part (a).
Express the quadratic form T as v Av, where A is a symmetric matrix. x² + 3y² + 5z² − 4xy+3yz + 10xz
(V). (16') Find the QR factorization of the matrix A=(x1,x2,x3), where 4 2 1 2 1 Xị = ,X2 = ,X3 = 2 1 2
Let B = {b,.b2} be bases for a vector space V, and suppose b, = 8c, - 2c2 and b2 = 9c, - 3c2. and C = %D a. Find the change-of-coordinates matrix from B to C. b. Find [x]c for x = - 3b, + 6b2. Use part (a). ... = C-B a.
(u1 + v1, U2 + v2) and au = (au1, 2), respectively. Let V = {(T,y)r, Y ER}, with addition and scalar multiplication defined as u + v = (u1, U2) and v = (v1, V2) and scalars a. Which of the following is true? where u = O A. k(lu) = (kl)u and 1u = u for all E V O B. (0,0) is the zero of V and (kl)u = k(lu) for all scalars k, l and u E V || O C. Addition is associative and k(u + v) ku + kv for all u, v E V and for all scalars k O D. 3(u + v) : 3u + 3v and the negative of (-2, 3) is (2, –3) O E. k(u + v) = ku + kv for u, v E V and scalar k, and addition is commutative Reset Selection
Let B and C be bases for R2. If B = {(-1, –1), (3, 4)} and the change-of-basis matrix from B to C is Pg-c find C.
Show that the vectors a = 3i−j+4k, b = i−3j−2k and c = 4i−3j+2k are linearlyindependent. Find numbers α, β and γ such that d = 2i + 3j − k can be expressedin the form d = αa + βb + γc.

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6 Let b₁=[2] b₂ = 3 4 [ C₁ = [ ² ] ² ₂ = 1²²] > V = [] (2 13 2 and C = { C₁₂ (₂} Find and consider the bases for R² given by B = { b₁,b₂} a) the change-of-coordinates matrix b) [V] B ; c) [V]c using the results from part a) and b)