Given the basis of R³ : B = {(1,0,−2), (2, -1, -1), (−1, 2, −3)}i. Find the vector in R³ whose coordinate vector with respect to basis B is (2,2,1).ii. What is the transition matrix that will change bases from B to the standard basis of R3³?iii. What is the transition matrix that will change bases from the standard basis of R³ to B.iv. Use the transition matrix to verify your answer for part i. of this question.

Given the basis of R³: B = {(1,0, -2), (2,-1,-1), (-1,2,-3)} i. Find the vector in R³ whose coordinate vector with respect to basis B is (2, 2, 1). ii. What is the transition matrix that will change bases from B to the standard basis of R³? iii. What is the transition matrix that will change bases from the standard basis of R³ to B.

Given the basis of R³: B = {(1,0, -2), (2,-1,-1), (-1,2,-3)} i. Find the vector in R³ whose coordinate vector with respect to basis B is (2, 2, 1). ii. What is the transition matrix that will change bases from B to the standard basis of R³? iii. What is the transition matrix that will change bases from the standard basis of R³ to B.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

(a) Determine the transition matrix corresponding to a change of basis from the standard basis {e1, e2} to the ordered basis {u1, u2}. Use this transition matrix to find the coordinates of x = (1, 1)T with respect to {u1, u2}. (b) Determine the transition matrix corresponding to a change of basis from the ordered basis {v1, v2} to the ordered basis {u1, u2}. Use this transition matrix to find the coordinates of z = 2v1 + 3v2 with respect to {u1, u2}.
5 Find the specified change-of-coordinates matrix. 7) Let B and C be bases for R2, where Find the change-of-coordinates matrix from B to C. b1 = ¹₁ -[3]- ¹₂ -[-+-C₁ -[3]· <₂2-[-₁6] b2 = C1 = C2 =
Let B = {b1, {b1, b2} and C ={c1, c2} be two bases for IR“, where 1 b2 = 3 3 C1 3 b1 10 7 22 67 what is the value of b d a If the change-of-coordinates matrix from C to B is ? -36 26 О-35 25 -34
Let B = {ü,,ü,}, B'={v,v,} be two bases in R, where %| ü, %3D 3 (a) Find the transition matrix from B' to B. (b) Find the transition matrix from B to B'.
Determine the standard matrix of a reflection in R² in the line 3x1 + 4x, = 0. 2
Find the change-of-coordinates matrix from B to the standard basis in R". 8 3 3 B= 7 -3 - 4 8 P8 =
5. 3 (a) Let A To which point does A map the point (2, –5)? To which point does A map the point (1,0)? 1 (b) Let B = To which point does B map the point (11, 8)? To 3 which point does B map the point (3, 4)? (c) Find the matrix which maps the point (2, –5) to the point (19, 13) and the point (1,0) to (7,9).
How did they get the numbers in front of the matrices such as (-1), (-2), (6) and so forth?