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5.4. Find the matrix of the orthogonal projection in R2 onto the line x1 = –2x2....
(1 point) Find the matrix A of the orthogonal projection onto the line L in R2...
(1 point) Find the matrix A of the orthogonal projection onto the line L in R2 that consists of all scalar multiples of the vector [63].
Problem 7. Let P R2 -> R2 be the orthogonal projection onto the line Li Let P2 R2 R2 be the orthogonal projection on...
Problem 7. Let P R2 -> R2 be the orthogonal projection onto the line Li Let P2 R2 R2 be the orthogonal projection onto the line L2: x32 2r2 0. 0. (1) What are the image and kernel of P2P What is the rank of P2P? Give a geometric description, without relying on the matrix of P2P (2) Find the matrix that represents P2P
Problem 7. Let P R2 -> R2 be the orthogonal projection onto the line Li Let...
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...
Problem 2. Recall that for any subspace V of R", the orthogonal projection onto V is...
Problem 2. Recall that for any subspace V of R", the orthogonal projection onto V is the map projy : RM → Rn given by projy() = il for all i ER", where Ill is the unique element in V such that i-le Vt. For any vector space W, a linear transformation T: W W is called a projection if ToT=T. In each of (a) - (d) below, determine whether the given statement regarding projections is true or false, and...
(1 point) Find the orthogonal projection of -1 -5 V = 9 -11 onto the subspace...
(1 point) Find the orthogonal projection of -1 -5 V = 9 -11 onto the subspace V of R4 spanned by -4 -2 -4. -5 X1 = and X2 1 -28 -4 0 projv(v)
4.4.3. Find the orthogonal projection of v (1,2,-1,2) onto the following subspaces: 12 20 1-1 01 ...
4.4.3. Find the orthogonal projection of v (1,2,-1,2) onto the following subspaces: 12 20 1-1 01 (a) the span of2 (b) the ma of the aris b3(0) the kernel of the matrix-2 Warning. Make sure you have an orthogonal basis before applying formula (4.42)! ; (d) the subspace orthogonal to a (1,-1,0,1)
4.4.3. Find the orthogonal projection of v (1,2,-1,2) onto the following subspaces: 12 20 1-1 01 (a) the span of2 (b) the ma of the aris b3(0) the...
17. The standard matrix of the the linear transformation that represents projection onto the vector 1...
17. The standard matrix of the the linear transformation that represents projection onto the vector 1 m onto the vector (9)}{-1 9 ®}1] (0}{-1) none of these [1 2 3] 18. The matrix O O 5 can be reduced (using elementary row operations) to [2 4 0 100] [120] 1 007 (A) 0 1 0 (B) 0 1 0 (0) 0 1 0 (D) none of these LO 0 1 LO 0 0 Lo o o 19. Which of the...
I will upvote! (2)()dz in the vector space Cº|0, 1] to find the orthogonal projection of...
I will upvote!
(2)()dz in the vector space Cº|0, 1] to find the orthogonal projection of f(a) – 332 – 1 onto the subspaco V (1 point) Use the inner product < 1.9 > spanned by g(x) - and h(x) - 1 proj) (1 point) Find the orthogonal projection of -1 -5 V = 9 -11 onto the subspace V of R4 spanned by -4 -2 -4 -5 X1 = and X2 == 1 -28 -4 0 -32276/5641 -2789775641 projv...
1. Find a 2x2 matrix A if for the vector v= [R], Av = [4 +38]...
1. Find a 2x2 matrix A if for the vector v= [R], Av = [4 +38] 2. For this problem, use matrices A = La ), B=1 _Jandc=lo 9]. Suppose that the matrices A and B commute (so AB=BA) and the matrices A and C commute. Find the entries for the matrix A. 3. Find a number a so that the vectors v = [3 2 a) and w = [2a -1 3] are orthogonal (perpendicular). 4. For the vector...
(a) Let T: R2 + R2 be counter clockwise rotation by 7/3, i.e. T(x) is the...
(a) Let T: R2 + R2 be counter clockwise rotation by 7/3, i.e. T(x) is the vector obtained by rotating x counter clockwise by 7/3 around 0. Without computing any matrices, what would you expect det (T) to be? (Does T make areas larger or smaller?) Now check your answer by using the fact that the matrix for counter clockwise rotation by is cos(0) - sin(0)] A A= sin(0) cos(0) (b) Same question as (a), only this time let T...
Problem 7. Let P R2 -> R2 be the orthogonal projection onto the line Li Let P2 R2 R2 be the orthogonal projection onto the line L2: x32 2r2 0. 0. (1) What are the image and kernel of P2P What is the rank of P2P? Give a geometric description, without relying on the matrix of P2P (2) Find the matrix that represents P2P
Problem 7. Let P R2 -> R2 be the orthogonal projection onto the line Li Let...
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...
Problem 2. Recall that for any subspace V of R", the orthogonal projection onto V is the map projy : RM → Rn given by projy() = il for all i ER", where Ill is the unique element in V such that i-le Vt. For any vector space W, a linear transformation T: W W is called a projection if ToT=T. In each of (a) - (d) below, determine whether the given statement regarding projections is true or false, and...
(1 point) Find the orthogonal projection of -1 -5 V = 9 -11 onto the subspace V of R4 spanned by -4 -2 -4. -5 X1 = and X2 1 -28 -4 0 projv(v)
4.4.3. Find the orthogonal projection of v (1,2,-1,2) onto the following subspaces: 12 20 1-1 01 (a) the span of2 (b) the ma of the aris b3(0) the kernel of the matrix-2 Warning. Make sure you have an orthogonal basis before applying formula (4.42)! ; (d) the subspace orthogonal to a (1,-1,0,1)
4.4.3. Find the orthogonal projection of v (1,2,-1,2) onto the following subspaces: 12 20 1-1 01 (a) the span of2 (b) the ma of the aris b3(0) the...
17. The standard matrix of the the linear transformation that represents projection onto the vector 1 m onto the vector (9)}{-1 9 ®}1] (0}{-1) none of these [1 2 3] 18. The matrix O O 5 can be reduced (using elementary row operations) to [2 4 0 100] [120] 1 007 (A) 0 1 0 (B) 0 1 0 (0) 0 1 0 (D) none of these LO 0 1 LO 0 0 Lo o o 19. Which of the...
I will upvote!
(2)()dz in the vector space Cº|0, 1] to find the orthogonal projection of f(a) – 332 – 1 onto the subspaco V (1 point) Use the inner product < 1.9 > spanned by g(x) - and h(x) - 1 proj) (1 point) Find the orthogonal projection of -1 -5 V = 9 -11 onto the subspace V of R4 spanned by -4 -2 -4 -5 X1 = and X2 == 1 -28 -4 0 -32276/5641 -2789775641 projv...
1. Find a 2x2 matrix A if for the vector v= [R], Av = [4 +38] 2. For this problem, use matrices A = La ), B=1 _Jandc=lo 9]. Suppose that the matrices A and B commute (so AB=BA) and the matrices A and C commute. Find the entries for the matrix A. 3. Find a number a so that the vectors v = [3 2 a) and w = [2a -1 3] are orthogonal (perpendicular). 4. For the vector...
(a) Let T: R2 + R2 be counter clockwise rotation by 7/3, i.e. T(x) is the vector obtained by rotating x counter clockwise by 7/3 around 0. Without computing any matrices, what would you expect det (T) to be? (Does T make areas larger or smaller?) Now check your answer by using the fact that the matrix for counter clockwise rotation by is cos(0) - sin(0)] A A= sin(0) cos(0) (b) Same question as (a), only this time let T...
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