Check the true statements below: A. The orthogonal projection of y onto v is the same...

Check the true statements below:

A. The orthogonal projection of y onto v is the same as the orthogonal projection of y onto cv whenever c≠0.

B. If the columns of an m×n matrix A are orthonormal, then the linear mapping x→Ax preserves lengths.

C. If a set S={u1,...,up} has the property that ui⋅uj=0 whenever i≠j, then S is an orthonormal set.

D. Not every orthogonal set in Rn is a linearly independent set.

E. An orthogonal matrix is invertible.

Expert Solution

Colby Messinger answered 1 year ago

Let W be a subspace of R^n, and P the orthogonal projection onto W. Then Ker...

Let W be a subspace of R^n, and P the orthogonal projection onto W. Then Ker P is W^perp.

2a. Find the orthogonal projection of [9,40,-29,4] onto the subspace of R4 spanned by [1,6,5,6] and...

2a. Find the orthogonal projection of [9,40,-29,4] onto the subspace of R4 spanned by [1,6,5,6] and [5,1,5,5]. Answer choices: [2,14,-15,7] [-32,13,-10,7] [0,9,12,6] [-5,-2,3,2] [-12,0,-9,-9] [-16,20,0,4] [27,29,29,21] [-3,1,2,7] [-23,7,-3,-9] [-15,5,-15,30] 2b. Find the orthogonal projection of [17,18,-10,24] onto the subspace of R4 spanned by [2,7,1,6] and [3,7,3,4]. Answer choices: [-34,-22,-29,-34] [-6,4,-2,0] [-12,36,21,33] [3,21,-3,24] [7,-14,-12,1] [5,3,32,45] [14,32,12,11] [9,13,18,11] [20,2,-3,19] [-2,-6,1,-7]

Using least squares, find the orthogonal projection of u onto the subspace of R4 spanned by...

Using least squares, find the orthogonal projection of u onto the subspace of R4 spanned by the vectors v1, v2, and v3, where u = (6, 3, 9, 6), v1 = (2, 1, 1, 1), v2 = (1, 0, 1 ,1), v3 = (-2, -1, 0, -1).

find the projection vector of the vector v = (2,3,5) onto the plane z = 2x...

find the projection vector of the vector v = (2,3,5) onto the plane z = 2x + 3y -1

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

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).)

Check only the correction statements below. Check the incorrect statements will result in losing a half...

Check only the correction statements below. Check the incorrect statements will result in losing a half of the points for a correct statement. ABC Inc. plans to expand the production by replacing the existing capital equipment. The following information is available. Last period This period Production (units) 3,000 3,500 materials (pounds) 3,000 3,000 cost per unit $0.80 $0.65 labor (hrs) 400 425 labor rate/hr $16.00 $16.00 capital equipment and its maintenance $12,000 $15,000 capital equipment fully depreciated, in periods 4...

Part A Which of the following statements are true regarding transformers? Check all that apply. Check...

Part A Which of the following statements are true regarding transformers? Check all that apply. Check all that apply. In a transformer, if the primary coil contains more loops than the secondary coil, then it is a step-up transformer. A transformer converts mechanical energy into electrical energy. A transformer is used to increase or decrease a direct current voltage. A transformer is used to increase or decrease an alternating current voltage. In a transformer, if the secondary coil contains more...

Let T : Rn -> Rm be a onto linear transformation. Select all the true statements...

Let T : Rn -> Rm be a onto linear transformation. Select all the true statements from the following list. (Incorrect choices will earn you negative points) For any y in Rm there exists a unique x in Rn such that T(x) = y For any y in Rm there is at most one x in Rn such that T(x) = y The range of T is the entire Rm For any y in Rm there is at least one...

check all of the statements that are true regarding keratinized stratified squamous epithelium

Which statements are true? Check all that apply: It is impossible to sell a part of...

Which statements are true? Check all that apply: It is impossible to sell a part of your ownership stake in a sole proprietorship. A sole proprietorship is subject to few government regulations. A sole proprietorship is easy to set up. All profits from a sole proprietorship are passed through to the owner for paying taxes. A sole proprietorship offers limited liability. A limited liability company is taxed like a _____ and its owners have _____ liability. partnership; limited partnership; unlimited...

Question