For parts ( a ) − ( c ), let u = 〈 2 , 4...
For parts ( a ) − ( c ), let u = 〈 2 , 4 , − 1 〉 and v = 〈 4 , − 2 , 1 〉.
( a ) Find a unit vector which is orthogonal to both u and v.
( b ) Find the vector projection of u onto v.
( c ) Find the scalar projection of u onto v.
Homework Answers
Exercise Set Chapter 3 Q1) Let u = (2, -2, 3), v = (1, -3, 4),...
Exercise Set Chapter 3 Q1) Let u = (2, -2, 3), v = (1, -3, 4), and w=(3,6,-4). a) Evaluate the given expression u + v V - 3u ||u – v| u. V lju – v|w V X W ux (v x W) b) Find the angle 8 between the vector u = (2,-2,3) and v = (1, -3,4). c) Calculate the area of the parallelogram determined by the vector u and v d) Calculate the scalar triple product...
5. Let u be a unit vector in R”. Let A = In – uu?. a)....
5. Let u be a unit vector in R”. Let A = In – uu?. a). Verify that A is symmetric, that is, AT = A. b) Verify that A is idempotent, that is, A2 = A. c) Let v be in vector in R”. Show that you can decompose v = w + z where w is a vector orthogonal to u and z is a vector parallel to u. (Hint: Consider the vector projection of v onto u....
Let R2 have the Euclidean inner product. (a) Find wi, the orthogonal projection of u onto...
Let R2 have the Euclidean inner product. (a) Find wi, the orthogonal projection of u onto the line spanned by the vector v. (b) Find W2, the component of u orthogonal to the line spanned by the vector v, and confirm that this component is orthogonal to the line. u =(1,-1); v = (3,1) (a) wi = Click here to enter or edit your answer (0,0) Click here to enter or edit your answer (b) 2 = W2 orthogonal to...
26 or 28 or both 25 28, find the vector projection of u onto v. Then write u In ExcTe wo orthogonal vectors, one of which is projyu. Insum of two orthogonal vect as a sum of two 26. (3.-7),2, 6) 2...
26 or 28 or both
25 28, find the vector projection of u onto v. Then write u In ExcTe wo orthogonal vectors, one of which is projyu. Insum of two orthogonal vect as a sum of two 26. (3.-7),2, 6) 27, u(8, 5), v 28, 2, 8), v-(9,-3 29 and 30, find the interior angles of the triangle with
25 28, find the vector projection of u onto v. Then write u In ExcTe wo orthogonal vectors, one of...
4 1|and b-l-2 Let A-13 a) Find the orthogonal projection p of b onto C(A) with its error vector. ...
4 1|and b-l-2 Let A-13 a) Find the orthogonal projection p of b onto C(A) with its error vector. b) Find the least squares approximation, £, to the solution vector x of Ai- c) The least squares error is defined to be the length of the vector b - AX. Find this vector and its length. d) What is the relationship between A, , and p?
4 1|and b-l-2 Let A-13 a) Find the orthogonal projection p of b onto...
Will rate once all is completed. 1) 2) 3) 4) (12 points) Find a basis of...
Will rate once all is completed.
1)
2)
3)
4)
(12 points) Find a basis of the subspace of R that consists of all vectors perpendicular to both El- 1 1 0 and 7 Basis: , then you would enter [1,2,3],[1,1,1] into the answer To enter a basis into WeBWork, place the entries. each vector inside of brackets, and enter a list these vectors, separated by commas. For instance if vour basis is 31 2 and u (12 points) Let...
Let u= -3 2 4 ; and let L denote the line thru the origin of R3 in the direction of u. The proj...
Let u= -3 2 4 ; and let L denote the line thru the origin of R3 in the direction of u. The projection of R3 onto L — denoted PL : R3 −→ R3 — is definded to be equal to the projection pu onto the vector u. You may assume that PL is a linear transformation. Find the standard matrix [PL] for PL.
(Section 11.3) Find the projection of u onto v and find the vector component of u...
(Section 11.3) Find the projection of u onto v and find the vector component of u orthogonal to v for: u=8 i+2j v = (2, 1, -2)
e, none of these 7. Let {1,..., up} be an orthogonal basis for a subspace W...
e, none of these 7. Let {1,..., up} be an orthogonal basis for a subspace W of R" and {...., } be an orthogonal basis for Wt. Determine which of the following is false. a. p+q=n b. {U1,..., Up, V1,...,0} is an orthogonal basis for R". c. the orthogonal projection of the u; onto W is 0. d. the orthogonal projection of the vi onto W is 0. e. none of these 8. Let {u},..., up} be an orthogonal basis...
(7) Let V be a finite-dimensional vector space over F, and PE C(V) In this question, we will show that P is an orthogonal projection if and only if P2P and PP It may be helpful to recal that P is the...
(7) Let V be a finite-dimensional vector space over F, and PE C(V) In this question, we will show that P is an orthogonal projection if and only if P2P and PP It may be helpful to recal that P is the orthogonal projection onto a subspace U if and only if (1) P is a projection, and (2) ran(P)-U and null(P)U (a) Prove that if P is an orthogonal projection, then P2P and P is self-adjoint Hint: To show...
Exercise Set Chapter 3 Q1) Let u = (2, -2, 3), v = (1, -3, 4), and w=(3,6,-4). a) Evaluate the given expression u + v V - 3u ||u – v| u. V lju – v|w V X W ux (v x W) b) Find the angle 8 between the vector u = (2,-2,3) and v = (1, -3,4). c) Calculate the area of the parallelogram determined by the vector u and v d) Calculate the scalar triple product...
5. Let u be a unit vector in R”. Let A = In – uu?. a). Verify that A is symmetric, that is, AT = A. b) Verify that A is idempotent, that is, A2 = A. c) Let v be in vector in R”. Show that you can decompose v = w + z where w is a vector orthogonal to u and z is a vector parallel to u. (Hint: Consider the vector projection of v onto u....
Let R2 have the Euclidean inner product. (a) Find wi, the orthogonal projection of u onto the line spanned by the vector v. (b) Find W2, the component of u orthogonal to the line spanned by the vector v, and confirm that this component is orthogonal to the line. u =(1,-1); v = (3,1) (a) wi = Click here to enter or edit your answer (0,0) Click here to enter or edit your answer (b) 2 = W2 orthogonal to...
26 or 28 or both
25 28, find the vector projection of u onto v. Then write u In ExcTe wo orthogonal vectors, one of which is projyu. Insum of two orthogonal vect as a sum of two 26. (3.-7),2, 6) 27, u(8, 5), v 28, 2, 8), v-(9,-3 29 and 30, find the interior angles of the triangle with
25 28, find the vector projection of u onto v. Then write u In ExcTe wo orthogonal vectors, one of...
4 1|and b-l-2 Let A-13 a) Find the orthogonal projection p of b onto C(A) with its error vector. b) Find the least squares approximation, £, to the solution vector x of Ai- c) The least squares error is defined to be the length of the vector b - AX. Find this vector and its length. d) What is the relationship between A, , and p?
4 1|and b-l-2 Let A-13 a) Find the orthogonal projection p of b onto...
Will rate once all is completed.
1)
2)
3)
4)
(12 points) Find a basis of the subspace of R that consists of all vectors perpendicular to both El- 1 1 0 and 7 Basis: , then you would enter [1,2,3],[1,1,1] into the answer To enter a basis into WeBWork, place the entries. each vector inside of brackets, and enter a list these vectors, separated by commas. For instance if vour basis is 31 2 and u (12 points) Let...
(Section 11.3) Find the projection of u onto v and find the vector component of u orthogonal to v for: u=8 i+2j v = (2, 1, -2)
e, none of these 7. Let {1,..., up} be an orthogonal basis for a subspace W of R" and {...., } be an orthogonal basis for Wt. Determine which of the following is false. a. p+q=n b. {U1,..., Up, V1,...,0} is an orthogonal basis for R". c. the orthogonal projection of the u; onto W is 0. d. the orthogonal projection of the vi onto W is 0. e. none of these 8. Let {u},..., up} be an orthogonal basis...
(7) Let V be a finite-dimensional vector space over F, and PE C(V) In this question, we will show that P is an orthogonal projection if and only if P2P and PP It may be helpful to recal that P is the orthogonal projection onto a subspace U if and only if (1) P is a projection, and (2) ran(P)-U and null(P)U (a) Prove that if P is an orthogonal projection, then P2P and P is self-adjoint Hint: To show...
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