4. In each case, check that {v1, ..., Vn} is a basis for R" and give the coordinates of the given vector b e R" with respect to that basis. 2 3 3 , V2 = 3 a. V = *b. Vị =|0 V2 =| 2 , V3 = | 3 |;b = 3 [2_ 2 2 3 C. V = V2 V3 2

4. In each case, check that {v1, ..., Vn} is a basis for R" and give the coordinates of the given vector b e R" with respect to that basis. 2 3 3 , V2 = 3 a. V = *b. Vị =|0 V2 =| 2 , V3 = | 3 |;b = 3 [2_ 2 2 3 C. V = V2 V3 2

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.1: Orthogonality In Rn

Problem 10EQ: In Exercises 7-10, show that the given vectors form an orthogonal basis for2or3. Then use Theorem...

See similar textbooks

Related questions

Q: 2. Find the coordinate vector of & = (2, 3) relative to the basis B = {(1,0), (1, 1)} in vector…

A: As per your query the solution of the question (2) has been done. For the solution of the problem…

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

Q: Write x as the sum of two vectors, one in Span fu1,u2,uz} and one in Span fu4}. Assume that fu, .u4}…

Q: 4 Let v, = -3, v 9 , v, =|11. Show that the given set of vectors in R' forms a basis or not? Also…

Q: [0 3 4 2]* v1 = [1 1 2 1]" %3D

Q: 2. Determine whether or not the set of vectors S = {v],v2, V3}, where Vj = (2, – 1, 1), v2 =…

A: Determine whether v1=2,-1,1, v2=1,2,3, v3=1,1,1 form basis or not. The set of vectors v1=x1,y1,z1,…

Q: 1 Which of the following is a basis of R4that includes the vectors and 1 ? 1 -1 1 1 1 1 1 1 -1 1 1 1…

Q: Find out Vector S= { V, V2, V3} is the Basis por R. if VI : ( 3,1,-4), Vz C2,s,6), V3 - C1,4,8) %3D…

A: Here we have to find whether v1 , v2 , v3 are basis of R3 or not.

Q: If vi, v2, ..., Vn are independent vectors in R", then they must form a basis of R". True False…

Q: Show that fu,, u,) is an orthogonal basis for R?. Then express x as a linear combination of the u's.…

Q: 1. Show that the vectors (1, 1,0), (1, 1, 1) and (1,0, 0) are a basis of R3. Find the coefficients…

Q: 2. Show that the set S = {P1, P2, P3} is a basis for P2 (space of polynomials of degree less or…

Q: Find the coordinate vector of [4, -2, 1] relative to the ordered basis B= ([0, 1, 1], [2, 0, 0], [0,…

Q: 8. Prove that ū = (2,2, 1), ī = (-1,0,1) and w = (-2,3,0) are a basis for R³. Use these three…

Q: If the vectorsV1,..., Vk form an orthonormal basis of OC", then they also form a basis of R*. O True…

Q: Let {e1, e2, ē3, ē4, ē5, ē6} be the standard basis in Rº. Find the length of the vector 4ē4 + 4ē, –…

A: Consider the given standard basis in R6 as, e1→,e2→,e3→,e4→,e5→,e6→ As we know that standard basis…

Q: 6. Let B= {(v,,V½, v½ } be a basis for R'. Use the Gram-Schmidt process to find an orthogonal basis.…

A: We need to find the orthogonal basis of R3 . The basis here is {v1 , v2 ,v3 } and we do not need to…

Q: 13. In P2, find the change-of-coordinates matrix from the basis B = {1 – 21 + t², 3 – 5t + 41², 2t +…

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

Q: 3 2 1 Let u [-]--[-]-[] -3 V 2 and w= 1 0 -1 4 (a) Show that B = {u, v, w} is an orthogonal basis.

A: The given vectors are: u=3-30, v=22-1, w=114. (a) To show: {u,v,w} is an orthogonal basis. (b) To…

Q: Find the coordinate vector of Prelative to the basis S= {P1P2P3} P1 = 1+x +x², p2 = x +x, p3 = x:p =…

A: Given: p=6-x-9x2p1=1+x+x2p2=x+x2p3=x2

Q: Suppose that a₁,a2,..., a, form a basis of R" and y = ₁²₁ +2₂₂ + ... + n Anan with 2; = 0. Prove…

Q: Given three linearly independent vectors V1 = (-1,4,-2,-4,-9), V2 = (-5,4,5,0,-4), Үз %3D (1,-3,9,…

A: The solution is given as

Q: Find a standard basis vector that can be added to the set (v1, v2} to produce a basis of R^3. v1…

A: The set (v1, v2} to produce a basis of R^3. v1 = (1, -1, 0) and v2 = (3, 1, -2)

Q: 4 Suppose v1, V2, V3 are vectors in R*, and the matrix A = v, v2 V3 has rank 1 W = Span{v1, V2, V3}…

Q: Define a basis v1, v2 of R² by vị obtained by applying the Gram-Schmidt Procedure to v1, v2? 2 by…

A: Consider the provided question, A Basis of a vector space. Let V be a subspace of Rn for some n. A…

Q: 5. Determine whether the following three vectors v, = (1, 2, 3, 4), = (0, 1, 0, -1) and v, = (1, 3,…

A: To determine the given vectors form of basis for or not.

Q: then the second coordinate of the vector in the basis is: (3,5,7) If B=((1,1,1),(1,0, 1), (0,1, 1))…

Q: 4. Find representation of the vector v = 2 – 2x+ 6x? with respect to following basis. {1+ 3x + 3x?;…

Q: snip

A: A basis for a vector space is a sequence of vectors with two properties The basis vectors are…

Q: Show that B = {v1, v2, v3} is an orthogonal basis for R3: v1 = (3,−3,0), v2 = (2,2,−1), v3 =…

Q: 7. In each part, show that the set of vectors is not a basis for R. (a) {(2, -3, 1), (4, 1, 1), (0,…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: Show that the set S = {(4,3, 2), (0, 3, 2), (0,0, 2)} is a basis for R* by showing that it spans R³…

A: Consider the provided question,

Q: Do the vectors v1 = (-3, 7) and v2 = (5, 5) form a basis for R²?

A: Given data:- Vector, v1=-3,7 and v2=5,5

Q: The vectors are an orthogonal basis for R2. -1 True False

A: Answer is False.

Q: If B = {(1,1,0), (0,1,1), (-1,0,2)} is a basis of R³, then the coordinate vector of v = (2,0,1) in…

A: Solve the following

Q: 4. Show whether the given vectors (1,0, 0), (0, 2, 0), (0, 0, 3), and (1, 1, 1) form a basis for R.…

Q: 1 Q.2) How can you show that the set{ 2 2} form basis of xy- plane in R3? 3

A: GIVEN SETS : The given sets are : 120,123 The augmented matrix is : 120123R2→R2-R1~120003

Q: Does the vectors v1 = (-3, 7) and v2 = (5, 5) form a basis for R2?

Q: 5. Find a basis of R' containing the vector (1, 1, -2)' and (1, 2, -1)".

Q: 2) Let S contain vectors of the form Then a basis for S would be: a b : a-5b-6c = 0 and…

Q: 4 2 If a basis for R3 is B = and if a vector in the standard basis is i = |-4|, find its 5…

A: We know, The set B of vectors in a vector space V is called a basis if every element of V can be…

Q: 7. If U¡¡ ‡ 0 are components of a tensor of the type (0, 2) and if the equation ƒU¡¡ + gU ji ³ = 0…

A: Given : Uij≠0 ,fUij+gUji=0 To Prove : f=g , Uij is skew symmetric

Q: ´) Consider the vectors - - (-) · · - () ₁ - - () a= 2 Do these vectors form a basis of R³? If yes,…

A: They form a basis for R3. Explanation is as follows

Q: The vectors e = and e2 are Select one: are the standard basis for R^2. O True False

A: Recall: Let V be a vector space . A linearly independent spanning set for V is called a Basis.…

Q: 2) Suppose the vı, V2, V3, V4 is a basis for a vector space V. Prove that vị + v2, Vz + V3, V3 + V4,…

Q: =,4} is linearly dependent. 2, V3). 3 000- 2 3 5. undant vector of R³ (b) {1, ₂} is linearly indepe…

Q: 2. 5. Consider twO basis of R: B = %3D -3 and (= 3. 5- 1- with respect to B, If a vector V E PR has…

A: The given 2 bases of ℝ2 are as follows. B=75, -3-1 and C=3-5, -12 Also, the coordinates of the…

Question

linear algebra 3,3 question 4 sub question a, and c

4. In each case, check that {v1, ..., Vn} is a basis for R" and give the coordinates of the
given vector b e R’ with respect to that basis.
3
3
а. Vi —
V2
3
4
1
1
*b. Vị =
V2 =
2
, V3 =
3 ; b
1
3
3
c. Vị =
V2 =
1
V3 =
1 |; b
2
1
1
2
1
V3
1
V4 =
1
1
; b
3
*d. V1 =
V2 =
1
4

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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 by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Define T:R2R2 by T(v)=projuv Where u is a fixed vector in R2. Show that the eigenvalues of A the standard matrix of T are 0 and 1.
Complete Example 2 by verifying that {1,x,x2,x3} is an orthonormal basis for P3 with the inner product p,q=a0b0+a1b1+a2b2+a3b3. An Orthonormal basis for P3. In P3, with the inner product p,q=a0b0+a1b1+a2b2+a3b3 The standard basis B={1,x,x2,x3} is orthonormal. The verification of this is left as an exercise See Exercise 17..
Use the inner product u,v=2u1v1+u2v2 in R2 and Gram-Schmidt orthonormalization process to transform {(2,1),(2,10)} into an orthonormal basis.
In Exercises 7-10, show that the given vectors form an orthogonal basis for2or3. Then use Theorem 5.2 to express was a linear combination of these basis vectors. Give the coordinate vector[w] ofwwith respect to the basis ={v1,v2}of 2or =v1,v2,v3 of3. v1=[111],v2=[110],v3=[112];w=[123]
Take this test to review the material in Chapters 4 and 5. After you are finished, check your work against the answers in the back of the book. Prove that the set of all singular 33 matrices is not a vector space.