Deck 6: Orthogonality and Least Squares

Question 1

Find the distance between the two vectors.

Answer 1

A

Question 2

Compute the dot product u · v.

Answer 2

A

Question 3

Find the distance between the two vectors.

Answer 3

A

Question 4

Find the distance between the two vectors.

Question 5

Compute the dot product u · v.

Question 6

Find the distance between the two vectors.

Question 7

Determine whether the set of vectors is orthogonal.

Question 8

Compute the dot product u · v.

Question 9

Find the distance between the two vectors.

Question 10

Express the vector x as a linear combination of the uʹs.

Question 11

Find a unit vector in the direction of the given vector.

Question 12

Express the vector x as a linear combination of the uʹs.

Question 13

Compute the dot product u · v.

Question 14

Compute the dot product u · v.
)2

Question 15

Find a unit vector in the direction of the given vector.

Question 16

Find the orthogonal projection of y onto u.

Question 17

Find the distance between the two vectors.

Question 18

Determine whether the set of vectors is orthogonal.

Question 19

Compute the dot product u · v.

Question 20

Find the distance between the two vectors.

Question 21

Solve the problem.

Question 22

Solve the problem.

Question 23

Data points: (2, 1), (3, 2), (7, 3), (8, 1)33)

Question 24

Find a least-squares solution of the inconsistent system Ax = b.

Question 25

Let W be the subspace spanned by the uʹs. Write y as the sum of a vector in W and a vector orthogonal to W.

Question 26

Find the orthogonal projection of y onto u.

Question 27

The given set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal basis for W.

Question 28

Write the word or phrase that best completes each statement or answers the question.

Question 29

The given set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal basis for W.

Question 30

Compute the length of the given vector.

Question 31

Find a QR factorization of the matrix A.

Question 32

Question 33

Find a least-squares solution of the inconsistent system Ax = b.

Question 34

Compute the length of the given vector.

Question 35

Solve the problem.
Data points: (5, -3), (2, 2), (4, 3), (5, 1)

Question 36

Let W be the subspace spanned by the uʹs. Write y as the sum of a vector in W and a vector orthogonal to W.

Question 37

Find a QR factorization of the matrix A.

Question 38

Given A and b, determine the least-squares error in the least-squares solution of Ax = b.

Question 39

Write the word or phrase that best completes each statement or answers the question.

Question 40

Question 41

Solve the problem.

Question 42

Solve the problem.

Question 43

Given: The data points (-2, 2), (-1, 5), (0, 5), (1, 3), (2, 5). 44) Suppose the errors in measuring the y-values of the last two data points are greater than for the
Other points. Weight these data points twice as much as the rest of the data.

Question 44

Given: The data points (-3, 2), (-2, 5), (0, 5), (2, 3), (3, 3). Suppose the errors in measuring the y-values of the last two data points are greater than for the
Other points. Weight these data points half as much as the rest of the data.