Question

first use Gram-Schmidt on x1, x2 to create orthogonal vectors v1 and v2 with the same...

first use Gram-Schmidt on x1, x2 to create orthogonal vectors v1 and v2 with the same span as x1, x2. Now use the formula

p =((y, v1)/(v1, v1))v1 + ((y, v2)/(v2, v2))v2

to compute the projection of y onto that span. Of course, replace the inner product with the dot product when working with standard vectors

2)

Compute the projection of y = (1, 2, 2, 2, 1)  onto span (x1, x2) where

x1 =(1, 1, 1, 1, 1)   x2 =(4, 1, 0, 1, 4)

The inner product to use is the usual dot product. (This will compute a best-fitting function that is quadratic with no linear term, fitting to the data (−2, 1),(−1, 2),(0, 2),(1, 2),(2, 1).)

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Which is required projection

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
first use Gram-Schmidt on x1, x2 to create orthogonal vectors v1 and v2 with the same...
first use Gram-Schmidt on x1, x2 to create orthogonal vectors v1 and v2 with the same span as x1, x2. Now use the formula p =((y, v1)/(v1, v1))v1 + ((y, v2)/(v2, v2))v2 to compute the projection of y onto that span. Of course, replace the inner product with the dot product when working with standard vectors 1) Compute the projection of y = (1, 2, 3)  onto span (x1, x2) where x1 =(1, 1, 1) x2 =(1, 0, 1) The inner...
Find the orthogonal projection of u onto the subspace of R4 spanned by the vectors v1,...
Find the orthogonal projection of u onto the subspace of R4 spanned by the vectors v1, v2 and v3. u = (3, 4, 2, 4) ; v1 = (3, 2, 3, 0), v2 = (-8, 3, 6, 3), v3 = (6, 3, -8, 3) Let (x, y, z, w) denote the orthogonal projection of u onto the given subspace. Then, the components of the target orthogonal projection are
3. a. Consider R^2 with the Euclidean inner product (i.e. dot product). Let v = (x1,...
3. a. Consider R^2 with the Euclidean inner product (i.e. dot product). Let v = (x1, x2) ? R^2. Show that (x2, ?x1) is orthogonal to v. b. Find all vectors (x, y, z) ? R^3 that are orthogonal (with the Euclidean inner product, i.e. dot product) to both (1, 3, ?2) and (2, 7, 5). C.Let V be an inner product space. Suppose u is orthogonal to both v and w. Prove that for any scalars c and d,...
Exercise 6. Consider the following vectors in R3 . v1 = (1, −1, 0) v2 =...
Exercise 6. Consider the following vectors in R3 . v1 = (1, −1, 0) v2 = (3, 2, −1) v3 = (3, 5, −2 )   (a) Verify that the general vector u = (x, y, z) can be written as a linear combination of v1, v2, and v3. (Hint : The coefficients will be expressed as functions of the entries x, y and z of u.) Note : This shows that Span{v1, v2, v3} = R3 . (b) Can R3 be...
Do the vectors v1 =   1 2 3   , v2 = ...
Do the vectors v1 =   1 2 3   , v2 =   √ 3 √ 3 √ 3   , v3   √ 3 √ 5 √ 7   , v4 =   1 0 0   form a basis for R 3 ? Why or why not? (b) Let V ⊂ R 4 be the subspace spanned by the vectors a1 and a2, where a1 =   ...
(a) Do the vectors v1 = 1 2 3 , v2 = √ 3 √ 3...
(a) Do the vectors v1 = 1 2 3 , v2 = √ 3 √ 3 √ 3 , v3=√ 3 √ 5 √ 7, v4 = 1 0 0 form a basis for R 3 ? Why or why not? (b) Let V ⊂ R 4 be the subspace spanned by the vectors a1 and a2, where a1 = (1 0 −1 0) , a2 = 0 1 0 −1. Find a basis for the orthogonal complement V ⊥...
Use the inner product (u, v) = 2u1v1 + u2v2 in R2 and the Gram-Schmidt orthonormalization...
Use the inner product (u, v) = 2u1v1 + u2v2 in R2 and the Gram-Schmidt orthonormalization process to transform {(?2, 1), (2, 5)} into an orthonormal basis. (Use the vectors in the order in which they are given.) u1 = ___________ u2 = ___________
Use the inner product u, v = 2u1v1 + u2v2 in R2 and the Gram-Schmidt orthonormalization...
Use the inner product u, v = 2u1v1 + u2v2 in R2 and the Gram-Schmidt orthonormalization process to transform   {(2, ?1), (2, 6)}  into an orthonormal basis. (Use the vectors in the order in which they are given.) u1 = u2 =
Use the inner product <u,v>= 2u1v1 + u2v2 in R2 and the Gram-Schmidt orthonormalization process to...
Use the inner product <u,v>= 2u1v1 + u2v2 in R2 and the Gram-Schmidt orthonormalization process to transform {(2, ?1), (2, 6)} into an orthonormal basis. (Use the vectors in the order in which they are given.) u1 = u2 =
Which of the following vectors are unit vectors with respect to the inner product: <(x1, x2,...
Which of the following vectors are unit vectors with respect to the inner product: <(x1, x2, x3) , (y1, y2, y3)> = 2x1y1 = 2x3y3 in R3? A. (1, 0, 0)   B. (1, 0, 0)/sqrt(2)   C. (1, 0, 1)/sqrt(2)    D. (1, 1, 0)/2 Select from the following: 1. Only A 2. Only B and D 3. Only A and C 4. All of A, B, C and D 5. None of the above Thank you!
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT