Homework Answers
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first
we find a basis for Plane W then we orthonormalize it using
gramschmidth.
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Find an orthonormal basis of the plane in R3 defined by the equation 2a yz0
Find an orthonormal basis for the plane viewed as a subspace of R3. Z (-1,0,2) (0,-1,0)...
Find an orthonormal basis for the plane viewed as a subspace of R3. Z (-1,0,2) (0,-1,0) (0,1,0)
Find an orthonormal basis for the subspace of R3 spanned by Extend the basis you found...
Find an orthonormal basis for the subspace of R3
spanned by
Extend the basis you found to an orthonormal basis for R 3 (by
adding a new vector or vectors). Is there a unique way to extend
the basis you found to an orthonormal basis of R3 ?
Explain.
Find an ONB (orthonormal basis) for the following plane in R3 2 + y + 3z...
Find an ONB (orthonormal basis) for the following plane in R3 2 + y + 3z = 0 First, solve the system, then assign parameters s and t to the free variables (in this order), and write the solution in vector form as su + tv. Now normalize u to have norm 1 and call it ū. Then find the component of v orthogonal to the line spanned by u and normalize it, call it ū. Below, enter the components...
Please attempt both questions. 5. Find an orthonormal basis for the plane viewed as a subspace...
Please attempt both questions.
5. Find an orthonormal basis for the plane viewed as a subspace of R3. Z (-1,0,2) (0,-1,0) (0,1,0) X 6. Determine if each basis is orthogonal. Further, is the basis orthonormal? (a) In the vector space R3 (i.e. column vectors in 3-space): 1 2 5 -3 (b) In the vector space that consists of polynomial functions of degree less than or equal to 2: {f(x) = 22 - 3, 9() = 4, h(x) = 2² +2}...
1.1. Sample Problems. 1. In R3, (a) Find an orthonormal basis which contains the vector (...
1.1. Sample Problems. 1. In R3, (a) Find an orthonormal basis which contains the vector ( 1, 0); (b) Find the component of the vector (1,1,1) in the direction of (1,0,1).
(i) Find an orthonormal basis {~u1, ~u2} for S (ii) Consider the function f : R3...
(i) Find an orthonormal basis {~u1, ~u2} for S
(ii) Consider the function f : R3 -> R3 that to each vector ~v
assigns the vector of S given by
f(~v) = <~u1, ~v>~u1 + <~u2; ~v>~u2. Show that it is a
linear function.
(iii) What is the matrix of f in the standard basis of R3?
(iv) What are the null space and the column space of the matrix
that you computed in the
previous point?
Exercise 1. In...
(10 pts) Find an orthonormal basis of the plane 21 - 4.62 - X3 = 0.
(10 pts) Find an orthonormal basis of the plane 21 - 4.62 - X3 = 0.
(1 point) Find an orthonormal basis of the plane x1 + 2x2 – x3 = 0....
(1 point) Find an orthonormal basis of the plane x1 + 2x2 – x3 = 0. -
4. Use the Gram-Schmidt Process to find an orthonormal basis for the subspace of R5 defined...
4. Use the Gram-Schmidt Process to find an orthonormal basis for the subspace of R5 defined by 2 S-span 0 2
(1 point) Find an orthonormal basis of the plane X1 + 4x2 – x3 = 0....
(1 point) Find an orthonormal basis of the plane X1 + 4x2 – x3 = 0. Answer: To enter a basis into WebWork, place the entries of each vector inside of brackets, and enter a list of these vectors, separated by commas. For instance, if your basis is 2 then you would enter [1,2,3], 3 [1,1,1) into the answer blank.
Find an orthonormal basis for the plane viewed as a subspace of R3. Z (-1,0,2) (0,-1,0) (0,1,0)
Find an orthonormal basis for the subspace of R3
spanned by
Extend the basis you found to an orthonormal basis for R 3 (by
adding a new vector or vectors). Is there a unique way to extend
the basis you found to an orthonormal basis of R3 ?
Explain.
Find an ONB (orthonormal basis) for the following plane in R3 2 + y + 3z = 0 First, solve the system, then assign parameters s and t to the free variables (in this order), and write the solution in vector form as su + tv. Now normalize u to have norm 1 and call it ū. Then find the component of v orthogonal to the line spanned by u and normalize it, call it ū. Below, enter the components...
Please attempt both questions.
5. Find an orthonormal basis for the plane viewed as a subspace of R3. Z (-1,0,2) (0,-1,0) (0,1,0) X 6. Determine if each basis is orthogonal. Further, is the basis orthonormal? (a) In the vector space R3 (i.e. column vectors in 3-space): 1 2 5 -3 (b) In the vector space that consists of polynomial functions of degree less than or equal to 2: {f(x) = 22 - 3, 9() = 4, h(x) = 2² +2}...
1.1. Sample Problems. 1. In R3, (a) Find an orthonormal basis which contains the vector ( 1, 0); (b) Find the component of the vector (1,1,1) in the direction of (1,0,1).
(i) Find an orthonormal basis {~u1, ~u2} for S
(ii) Consider the function f : R3 -> R3 that to each vector ~v
assigns the vector of S given by
f(~v) = <~u1, ~v>~u1 + <~u2; ~v>~u2. Show that it is a
linear function.
(iii) What is the matrix of f in the standard basis of R3?
(iv) What are the null space and the column space of the matrix
that you computed in the
previous point?
Exercise 1. In...
(10 pts) Find an orthonormal basis of the plane 21 - 4.62 - X3 = 0.
(1 point) Find an orthonormal basis of the plane x1 + 2x2 – x3 = 0. -
4. Use the Gram-Schmidt Process to find an orthonormal basis for the subspace of R5 defined by 2 S-span 0 2
(1 point) Find an orthonormal basis of the plane X1 + 4x2 – x3 = 0. Answer: To enter a basis into WebWork, place the entries of each vector inside of brackets, and enter a list of these vectors, separated by commas. For instance, if your basis is 2 then you would enter [1,2,3], 3 [1,1,1) into the answer blank.
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