Let: v = the matrix: -20 -15 11 18 Write v as a linear combination of the vectors in the following basis of R4: B = 15 9 1 1 9 2 -3 -1 -5 -1 2 1 -11 -5 1 0 (These are four vertical 4x1's, separated by commas.) It is not necessary to verify that B is a basis.

Let: v = the matrix: -20 -15 11 18 Write v as a linear combination of the vectors in the following basis of R4: B = 15 9 1 1 9 2 -3 -1 -5 -1 2 1 -11 -5 1 0 (These are four vertical 4x1's, separated by commas.) It is not necessary to verify that B is a basis.

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: Determine whether is in the column space of A, and if so, express as a linear combination of the…

A: A vector belongs to the column space of matrix if the vector can be expressed as a linear…

Q: Write down a basis of R 4 where you don't use any of the standard unit vectors (e1, ... , e4). Show…

Q: Find all values of h so that the set of vectors 4 forms a basis for R3? Justify your answer.

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: For the matrix A below, find a nonzero vector in Nul A and a nonzero vector in Col A. 3 2 A = - 12…

A: Given, A=3211-12-60-126-2-1026.

Q: Consider the alternative basis 7₁, 72, 73 of (column) vectors for R³ where: v₁ = e₁-e₂+€3, √¹₂ = 2 +…

Q: Express the vector (4, 7, -2) as a combination of the standard basis vectors i = (1, 0, 0), 3 = (0,…

Q: Three vectors (PQ), (PR), (QR) have been written in matrix form as shown below: 2 -17 PQ1 1 PR = -2…

Q: Given three linearly independent vectors V₁ = (2, 10,0,3,7), V₂ = (-5,2,-3,3,-4), V3 = (-4,-5,…

A: To complete the given three linearly independent vectors to a basis in ℝ5 using the first two…

Q: Write v as the sum of two vectors, one in Span (u₁) and one in Span (u2,03,04). Assume that (u₁...4}…

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: Let B, D be the following two bases of R³: B = D= 0 0 -2 2 a) Find the change of coordinates matrix…

Q: The vectors V, -5 [29] 24 [04.0₂ Write span R2 but do not form a basis. Find two different ways to…

Q: Determine if vector b is a linear combination of the vectors formed from the columns of matrix A and…

Q: Let B, D be the following two bases of R³: -1 B = D= a) Find the change of coordinates matrix Po-s…

A: Solution is below.

Q: You are given the following vectors in terms of their components in the i, j, k basis: A=11+2j+-1k B…

A: Since you have posted a multi subparts question according to guidelines I will solve…

Q: Consider the following vectors: -3 6 = | b2 || b3 where b1, b2 and b3 are any real numbers. Show…

Q: Consider the coordinate vectors -3, [als [B]s= %3D 4. 6. (0) Find B if S is the basis in: : 3 3 -12…

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

Q: For the matrix N = Answer: 9 22 4 3 7 1 4 11 3 etry this question below find three different…

Q: Solve if the following vectors is a basis: 1. Ả = in – 3iz + 2i3 B = 21₁ 41₂ - 13 C = 3i₁ +21₂ - 13…

Q: Express v = (-i, 2 + i, -1) as a linear combination of the following basis vectors given below.…

A: According to the given information it is required to express the given vector v as a linear…

Q: Find a vector orthogonal to both v and W. v = 3i + 2j + k, w = -5i - 5j - k 3i - 2j - 5k -3i + 2j -…

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

Q: Consider R is an inner product space with the inner product is defined as = U1V1 + 2u2v2 + 3uzV3…

A: We need to transform the basis w1, w2, w3 to an orthonormal basis z1, z2, z3 For a basis w1, w2, w3,…

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: Oa + Ob+0c + 4d la + (-1) b+ (-2) c +4d Oa + 1b + (-2) c + 5d la + (-1) b+ (-2) c + 2d 2a + 1b+…

A: 1) Let Tabcd=0a+0b+0c+4d1a+(-1)b+(-2)c+4d0a+1b+(-2)c+5d1a+(-1)b+(-2)c+2d2a+1b+(-10)c+4d To Find:…

Q: Define B = {b1, b2} and C = {c1,c2} for the vectors given below. First show that B and C are both…

Question

Let:
v = the matrix:

-20

-15

Write v as a linear combination of the vectors in the following basis of R⁴:

B =

15	9	1	1
9	2	-3	-1
-5	-1	2	1
-11	-5	1	0

(These are four vertical 4x1's, separated by commas.)

It is not necessary to verify that B is a basis.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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

Step 2

Step 3

Step 4

Step 5

Step 6

Step by step

Solved in 6 steps with 6 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Find a basis B for the span of the given vectors. 8 -8 HAD 1 B = -1 300 ↓ 1 2 -2
Find a basis for the set of all vectors of the form below, where a, b, c are real numbers. [ a-2b+5c, 2a+5b-8c, -a-4b+7c, 3a+b+c]
Consider two bases B = {b1,b2} andC : such that bị = cq – 4c2 and b2 = 6c1 – 5c2. Find the change-of- coordinates matrix from B to C. {C1, c2} for a vector space V, %3D %3D 6. 4 -5 1 6 4 5 1-4 6. -5 1 -4 -5
Let u = (1,3, 5) and v = (-4,3, –7) be vectors in R3. (a) Find u + v. (b) Express u in terms of the standard basis vectors in R3. (c) Find -3u.
Find the representation of (9, -2, -3) in each of the following ordered bases. Your answers should be vectors of the general form . a. Represent the vector (9, -2, -3) in terms of the ordered basis B = {i,j,k}. [(9,-2,-3)]B= b. Represent the vector (9, -2, -3) in terms of the ordered basis C = {3, e1, e2}. [(9,-2,-3)] c = c. Represent the vector (9, -2, -3) in terms of the ordered basis D= {-2, -1, e3}. [(9,-2,-3)]D =
Determine whether the following vectors form a basis of R4: 2 4 8 -2 4 -8
Solve (b)
Find a basis for the row space of A, consisting of vectors, that are row vectors of A. Where 1 2 -1 3 3 A = 5 1 1 |-1 0 -2 7