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}.
d) Transform the system of equations if possible: x'= 1 2 1x. 2 11 into a decoupled system, by means of a similarity transformation, and compute a fundamental matrix of it.
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 u (a) Find the transition matrix T corresponding to the change of basis from (es. e. e) to (₁,₂,₂) (b) Find the coordinates of the vector x = 100 -2 with respect to the basis (₁, ₂, 3)
Orthogonally dlagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. 10-61 A) B) 3WT3 -2//13 P = D) C) 3WT3 2N13 D- P = Lunonal to W.
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).
Let B= ((1, 3), (-2,-2)) and 8' = ((-12, 0), (-4, 4)) be bases for R2, and let be the matrix for T: R2 R2 relative to B. (a) Find the transition matrix P from B' to B. p= (b) Use the matrices P and A to find [v] and [7(v)le, where [vla [-1 31. [v] = [T(v)18- 11 p-1 11 (c) Find pand A' (the matrix for 7 relative to 8). 41 41 (d) Find [7(vil bwo ways. (7)=P(7) [vila Al- 11 11
How did they get the numbers in front of the matrices such as (-1), (-2), (6) and so forth?