1. Compute the orthogonal complement of each of the following subspace of the given vector space.(a) W = Span{(1,5, 3), (–3, 5, 7)} in R³.(b) W = Span{(1, 2, 0, 0, 7), (0, 0, 0, 2, 3)} in R5

We have to find orthogonal complement of given subspace: Concept: If x is orthogonal vector to…

Answered: 1. Compute the orthogonal complement of…

1. Compute the orthogonal complement of each of the following subspace of the given vecto (a) W = Span{(1,5, 3), (–3, 5, 7)} in R³. (b) W = Span{(1, 2, 0, 0, 7), (0, 0, 0, 2, 3)} in R5

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 59CR

See similar textbooks

Related questions

Q: Find a basis for the subspace of R3 spanned by S = {(2,3, -1), (1,3, -9), (0,1,5)}

Q: Let S be the subspace of R¹ consisting of the solutions to the following system of equations:…

Q: Find a basis for the subspace of R* spanned by S. s 3D {(2, 5, -3, -2), (-2, -3, 2, -3), (1, 3, —2,…

Q: Let W be the subspace spanned by the vectors (1,2, 0, 3) and (2, 1,3,0). Find : a basis for W+.

A: Given that W is a subspace spanned by the vectors 1 , 2 , 0 , 3 and 2 , 1 , 3 , 0 . i.e., W = span1…

Q: Let Hspan {(-3,-1,-2), (17, -1, 10), (-5, 0, -3)}. A basis for the subspace HCR³ is { vector

Q: Prove that the set of vectors of the form (a, b, c) where b = a +c is a subspace of R³.

A: According to the given information, it is required to prove that:

Q: Which one of the followings is NOT the subspace of R2 ? W = {(0,–2a): a e R} - W = {(2a, a): a e R}…

A: To find which one is not a subspace.

Q: Find the dimension of the subspace spanned by the given vectors: u₁ = (1, 3, -2,5), u₂ = (0, 1,-1,…

Q: 1 . Determine which of the following subspaces of R³ are identical: U₁ = span[(1, 1, -1), (2,3,-1),…

Q: (14) Find the dimension of the subspace H = a + 4b+c+2d a + 2b + d a +5b+c+3d b+d = ahader } : a, b,…

Q: V₁ 1₁3 G a. Is w in (₁,₂,3)? How many vectors are in (V₁, V₂, Va)? b. How many vectors are in…

A: Three vectors v1,v2,v3 are given. (a) First one needs to check whether another vector w is in the…

Q: Find a basis for each subspace... [5r-3s, 2r, 0, -4s] ER^4:r and s are scalars

Q: Suppose that S is a subspace in R spanned by all solutions to -x,+3x,3D0. Then its orthogonal…

A: See the detailed solution below.

Q: 1. Find a basis for the subspace of R4 spanned by the vectors (1,1,-4,-3), (2,0,2,-2), (2, -2,3,2)

A: Solution:-

Q: 8. Let W denote the subspace of R5 consisting of all the vectors having coordinates that sum to…

A: Consider the provided question,Write the given vectors into a matrix as below,

Q: Find the dimension of the subspace of all vectors in R3 whose first and third entries are equal.

Q: 7. Find a basis for, as well as the dimension of the subspace of R* generated by the vectors (1, -1,…

Q: (11) Find a basis for the orthogonal complement of the subspace of R" spanned by the vectors V1 =…

A: We have to solve given problem;

Q: 3. Is the set of all vectors (x, y) in R2 with the usual addition and scalar multiplication, a…

Q: 2. Consider the vectors v₁ = [1, 1, 1] and v2 = [1, 0, 0]. These two vectors define a 2-dimensional…

A: Let us find the projections.

Q: Consider the subspace 3 12 3 -2 U = span{ 7 -2 -7 3 6. of R4. Create a basis 3 -2 { 3 -2 ,x} -3 for…

A: Consider the provided question, Consider the subspace U=span-3-27-7, 12-2-73, 3-2-46 of R4.Create a…

Q: -1 < x < 2 (100< y< 0 Transformation of the region under w=1/z.

A: Let w = u + i v and z = x + i y, then w=1z ⇒u+iv=1x+iy ⇒u+iv=1x+iy×x-iyx-iy=x-iyx2+y2 Comparing the…

Q: Consider the subspace S of the Euclidean inner product space R4 spanned by the vectors v₁ =…

Q: Find a basis for the subspace of R³ spanned by S. S = {(1, 5, 7), (-1, 6, 7), (2, 6, 1)}

A: Write the given set of elements as the rows to form a 3x3 matrix. The space spanned by the rows of…

Q: 2. Find the dimension of the subspace of R³ spanned by the following set of vectors. {(1,5, 6),…

Q: Determine if the given Vector Subspace is LINEARLY INDEPENDENT IN THE REQUESTED VECTOR SPACE:

Q: 6. (a) Determine whether the set of all vectors of the form (a,b,c), where b = a+c, is a subspace of…

A: To show the subset W is a subspace , we need to show that (a) 0∈W (b) For every w1 , w2∈W , we have…

Q: Find a basis of the subspace of R5 spanned by the following vectors: 4 1 -1 8 6 6 -2 2 12 16 -1 -2 2…

Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

1. Compute the orthogonal complement of each of the following subspace of the given vector space.
(a) W = Span{(1,5, 3), (–3, 5, 7)} in R³.
(b) W = Span{(1, 2, 0, 0, 7), (0, 0, 0, 2, 3)} in R5

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Trending now

This is a popular solution!

Step by step

Solved in 7 steps with 6 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Vector Space$

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

Find a basis for R2 that includes the vector (2,2).
Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors {vu,wv,uw} is linearly independent or linearly dependent.
Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
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.
Prove that in a given vector space V, the zero vector is unique.
Find the bases for the four fundamental subspaces of the matrix. A=[010030101].
Let B={(0,2,2),(1,0,2)} be a basis for a subspace of R3, and consider x=(1,4,2), a vector in the subspace. a Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B. b Apply the Gram-Schmidt orthonormalization process to transform B into an orthonormal set B. c Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B.
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=3, W={[a0a]}
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=3, W={[aba+b+1]}
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=3, W={[aba]}
Let A be an mn matrix where mn whose rank is r. a What is the largest value r can be? b How many vectors are in a basis for the row space of A? c How many vectors are in a basis for the column space of A? d Which vector space Rk has the row space as a subspace? e Which vector space Rk has the column space as a subspace?
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=M22,W={[abcd]:adbc}