4 -7 -5 The change of coordinates matrix from basis B to basis C of R' is given by P = C-B -4 2 -3 9. 7 -8 2. The coordinates of v E R³ relative to the basis B are given by [v]B 4 Find [v]c, the coordinates of v 3 relative to the basis C. Ex: 6 [v]c =

4 -7 -5 The change of coordinates matrix from basis B to basis C of R' is given by P = C-B -4 2 -3 9. 7 -8 2. The coordinates of v E R³ relative to the basis B are given by [v]B 4 Find [v]c, the coordinates of v 3 relative to the basis C. Ex: 6 [v]c =

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

Related questions

Q: Find a basis for R that includes the vectors (2, -1, 5) and (4, 5, -5) {(2, -1, 5), (4, 5, -5), )}

A: Idea is we try to find a vector which is not in the span of given two vectors now collection of…

Q: In P2, find the the standard basis C = {1,t,t²}. Then find the B-coordinate vector for − 4 + 10t −…

A: We know that is a vector space consisting of the set of all the polynomials of degree lessthan or…

Q: part (d) and (e)

Q: Find the vector x determined by the given coordinate vector [x]g and the given basis B. - 1 2 5 - 8…

A: Find the vector x determined by the given coordinate vector [x], and the given basis B.

Q: Determine whether or not the given vectors form a basis of R4 V1 %3D (-2, 6, 2, 4), v2 3D (1,0,…

A: To Determine: whether or not the given vectors form a basis of R4 Given: we have v1=-2,6,2,4…

Q: The coordinate vector of the vector (-4,3,1) in the basis B={u=(1,1,1); v= (1,0,1); w= (0,0,1) } is…

Q: Answer considering the matrix with the given vectors as its columns

Q: Answer considering the matrix with th e given vectors as its columns

A: Given: The given matrices are, Assume the linear combination as follows,

Q: 5. Do the vectors {(1, -2, 1), (2,-3, 1), (5, -8, 1), (-1, 1,2)} form a basis for R'? Provide a…

Q: The vectors v1, v2 and v3 form an orthonormal basis for R3 where v1:=vector([0,0,-1]);…

Q: Find the coordinate vector [x] of x relative to the given basis B= (b₁,b₂}. 1: 2 MAM-HA = -5 b₁ -3…

Q: Consider the three basic vectors: (2,1,0,-1),(-1,1,1,1),(2,7,4,1) a. give two vectors that are in…

A: Given the three basic vectors: (2,1,0,-1),(-1,1,1,1),and (2,7,4,1) We have…

Q: and v3 2 Complete parts (a) and (b). Let P = -3 -4 V1 = V2 = 4 5 6 2 5 a. Find a basis fu,, uz, uz)…

Q: Let uj = U2 = V1 = V2 and va Let U = {u, uz) and let V = {v, Va Va). (a) Let eju +Cu2 Solve for e…

Q: Find w, where w3 = 1 + i. i? = -1.

Q: - 3 HG 4 4 5 1 2 Let P = - 3 1 3 - 1 W₁ = -5 0 - 4₂ = a. Find a basis (U₁, U₂, U3} for R³ such that…

A: (a)It is given that, P is the change of coordinates matrix from to .Also, the values are:So, using…

Q: Find the vector x determined by the coordinate vector ---(DBE) 8 and the basis B = 0 XB = The vector…

Q: Help!! Please answer correctly

A: a)Let v=⎣⎢⎡xyz⎦⎥⎤∈R3Let cB=⎣⎢⎡cB1cB2cB3⎦⎥⎤ be the cordinate vector of v with respect to…

Q: V1 || The vectors 2 -5 O " V₂ = -5 2 7 form a basis for R³ if and only if k# and V3 = -16 -2 B k

Q: The coordinate vector of the vector (-4,3,1) in the basis B = {u= (1,1,1); v = (1,0,1); w=(0,0,1) }…

A: We have to find the coordinate vector of the vector -4, 3, 1 in the basis B=u=1,1,1; v=1,0,1;…

Q: Determine the orthogonal basis by calculating w1 = w2 - [(23,5)] - [(-9,-2)] and calculating w2 Now…

Q: 1. Say whether the following vectors are linearly independent and whether the vectors form a basis…

A: Given Data: Let us consider the given data, c 2,-2,1,0,2,-2,2,0,-1d 1,1,1,1,-1,-1,-1,1,-1,-1,-1,1…

Q: (a) Given S={(1,-5,4), (11,6,-1), (2,3,5)} the set of vectors in R³. Determine whether (i) S spans…

Q: Determine whether the given vectors are form a basis of 3 V₁ = (3,-1,2), 2 (6, -2,4), V3 = (5,3,…

Q: Find the coordinate vector [x]g of x relative to the given basis B = {b₁,b₂, b3}. 1 b₁ = -1, b₂ = -5…

Q: Let B = {b₁,b2} be the basis in R² pictured below. a = If the coordinate vectors [u] O C = 12 d = bl…

Q: 2.) Determine whether S = {(G).(10).(2,12,6)} is a basis for R. If it i write u = (6,3,6) as a…

Q: Find the coordinate vector [x]R of x relative to the given basis B= {b1, b2, b3}. 1 4 1 - 6 b, 0 ,…

Q: E Let p 8x + 4x + 3. Find the coordinate vector of p relative to the following basis for P2, Pi = 1,…

A: We have to find the coordinate vector of P.

Q: Show that both R and R2 may be covered by countably many open balls.

Q: 31. Consider the set of vectors in Mn: 3 2 7 2 9 3 4 6. S = 3 It follows that (A) S is a basis for…

Q: Find the coordinate vector [x]B of x relative to the given basis B= {b1, b2} b1 b2 - 3 %3D X = - 10…

Q: In P2, find the change-of-coordinates matrix from the basis B= {1 − 2t + 1²,3 −5t + 4t²,2 − 2t +…

Q: Determine the dimension of the vector space. M2,3 STEP 1: Determine the number of linearly…

Question

4
-7
-5
The change of coordinates matrix from basis B to basis C of R' is given by P =
C-B
-4
2
-3
9.
7
-8
2.
The coordinates of v E R³ relative to the basis B are given by [v]B
4 Find [v]c, the coordinates of v
3
relative to the basis C.
Ex: 6
[v]c =

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Determinant$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

The coordinate vector of the vector (-4,3,1) in the basis B = {u= (1,1,1); v = (1,0,1); w= (0,0,1) } is: O A. (1,-4,3) OB. (-4,3,1) OC. (3,- 7,5) O D. (2,-1,1)
2. Find the coordinate vector [x] of a relative to the given basis B = {b₁,b2, b3} . b₁ = -1 , b₂ = -3 4 9 b3 = 2 -2 4 ,x= 8 -9 6
The coordinate vector of the vector (-4,3,1) in the basis B = {u= (1,1,1); v= (1,0,1); w= (0,0,1) } is : O A. (2,-1,1) OB. (-4,3,1) O C. (1,-4,3) D. (3,- 7,5)
The standard basis & (e₁,e₂) and two custom bases B (b₁,b₂} and C (c₁, c₂} for R² are shown in the figures below. Standard basis S= (₁, ₂) 4 a. Find the change of basis matrix from custom B-coordinates to standard S-coordinates. [id] = id= -2 b Find the change of basis matrix from custom C-coordinates to standard S-coordinates [id] = -1 -1 -1 c. Find the change of basis matrix from B-coordinates to C-coordinates -3 -1/12 1/4 d. Find the change of basis matrix from C-coordinates to B-coordinates. 3 2 1 -1 -2 -9 b2 -3-2-1 82 el bl 1 2 3 b1 X Custom basis B = {b₁,b₂) |id|s [id Standard basis S= (0₁,0₂} a 3 2 1 -1 -2 -9 c2 -3 -2 -1 G2 62 217 el [id] ↑ cl 12 2 3 61 H x Custom basis C (C₁, C₂)
Q16 Please provide justified answer asap to get a upvote
Find the coordinate vector of v relative to the basis S = {v1, V2, V3 } for R3. v = (42, 34, 24); v1 = (4, 0, 0), v2 = (5, 5, 0), v3 = (8, 8, 8). (v)s =( i ). i i
Find the change-of-coordinates matrix from B to the standard basis in R". 8 3 3 B= 7 -3 - 4 8 P8 =
Find the coordinate vector of v relative to the basis S = {v1, V2, V3 } for R3. v = (41, 39, 21); v1 = (7, 7, 7). (2, 0, 0), v2 = (6, 6, 0), v3 = (v)s=( i i i ).
Solve (b)
Find the vector x determined by the given coordinate vector [x] and the given basis B. Illustrate the answer with a figure. 2 -CH-)--[] [X]B = -1 B= 1 1 3 2