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Section A Answer ALL questions in this section. Each question in this section is worth 5%....
All vectors and subspaces are in R”. Mark each statement True or False. Justify each answer....
All vectors and subspaces are in R”. Mark each statement True or False. Justify each answer. Complete parts (a) through (e) below. a. If W is a subspace of R" and if y is in both W and wt, then y must be the zero vector. If v is in W, then projwv = Since the wt component of v is equal to v the w+ component of v must be A similar argument can be formed for the W...
Find the orthogonal projection of v = |8,-5,-5| onto the subspace W of R^3 spanned by...
Find the orthogonal projection of v = |8,-5,-5| onto the
subspace W of R^3 spanned by |7,-6,1| and |0,-5,-30|.
(1 point) Find the orthogonal projection of -5 onto the subspace W of R3 spanned by 7 an 30 projw (V)
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...
Problem 4. Let V be the vector space of all infinitely differentiable functions f: [0, ]...
Problem 4. Let V be the vector space of all infinitely differentiable functions f: [0, ] -» R, equipped with the inner product f(t)g(t)d (f,g) = (a) Let UC V be the subspace spanned by B = (sinr, cos x, 1) (you may assume without proof that B is linearly independent, and hence a basis for U). Find the B-matrix [D]93 of the "derivative linear transformation" D : U -> U given by D(f) = f'. (b) Let WC V...
Section 5.5 Orthonormal Sets: Problem 4 Previous Problem Problem List Next Problem (1 point) Find the...
Section 5.5 Orthonormal Sets: Problem 4 Previous Problem Problem List Next Problem (1 point) Find the orthogonal projection of 11 -14 V= 9 14 onto the subspace V of R4 spanned by 5 0 2 -1 X1 = and x2 = -1 -2 4 0 projy(v) =
Please attempt all questions. 2. Use the polynomial inner product to find the projection of f(*)...
Please attempt all questions.
2. Use the polynomial inner product to find the projection of f(*) onto g(x). (a) f(x) = -12 -1, 9(20) = ? (b) f(x) = 2x2, g(x) = 2+1 (C) f(c) = -1-1, g(x) = r2 +3 3. Use the continuous function on the interval [0,1) inner product to find the projection of f(x) onto g(2). (Feel free to use an integral calculator. I use wolfram alpha. Just make sure to type the problem in carefully)....
Hi, could you post solutions to the following questions. Thanks. 2. (a) Let V be a vector space on R. Give the definition of a subspace W of V 2% (b) For each of the following subsets of IR3 sta...
Hi,
could you post solutions to the following questions. Thanks.
2. (a) Let V be a vector space on R. Give the definition of a subspace W of V 2% (b) For each of the following subsets of IR3 state whether they are subepaces of R3 or not by clearly explaining your answer. 2% 2% (c) Consider the map F : R2 → R3 defined by for any z = (zi,Z2) E R2. 3% 3% 3% 3% i. Show that...
Please attempt both questions 3. Use the continuous function on the interval (0,1) inner product to...
Please attempt both questions
3. Use the continuous function on the interval (0,1) inner product to find the projection of f(x) onto g(x). (Feel free to use an integral calculator. I use wolfram alpha. Just make sure to type the problem in carefully). (a) f(x) = -22 - 1, g(x) = -2 (b) f(x) = 2r?, g(x) = 2+1 (e) f(x)=-1-1, g(x) = x2 +3 4. Consider 3-space with the dot product. Your subspace S will be the plane z...
(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...
Section 5.5 Orthonormal Sets: Problem 6 Previous Problem Problem List Next Problem 1 (1 point) Use...
Section 5.5 Orthonormal Sets: Problem 6 Previous Problem Problem List Next Problem 1 (1 point) Use the inner product < f, g >= . f(x)g(x)dx in the vector space C°[0, 1] to find the orthogonal projection of f(x) = 6x2 + 1 onto the subspace V spanned by g(x) = x - and h(x) = 1. projy(f) =
All vectors and subspaces are in R”. Mark each statement True or False. Justify each answer. Complete parts (a) through (e) below. a. If W is a subspace of R" and if y is in both W and wt, then y must be the zero vector. If v is in W, then projwv = Since the wt component of v is equal to v the w+ component of v must be A similar argument can be formed for the W...
Find the orthogonal projection of v = |8,-5,-5| onto the
subspace W of R^3 spanned by |7,-6,1| and |0,-5,-30|.
(1 point) Find the orthogonal projection of -5 onto the subspace W of R3 spanned by 7 an 30 projw (V)
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...
Problem 4. Let V be the vector space of all infinitely differentiable functions f: [0, ] -» R, equipped with the inner product f(t)g(t)d (f,g) = (a) Let UC V be the subspace spanned by B = (sinr, cos x, 1) (you may assume without proof that B is linearly independent, and hence a basis for U). Find the B-matrix [D]93 of the "derivative linear transformation" D : U -> U given by D(f) = f'. (b) Let WC V...
Section 5.5 Orthonormal Sets: Problem 4 Previous Problem Problem List Next Problem (1 point) Find the orthogonal projection of 11 -14 V= 9 14 onto the subspace V of R4 spanned by 5 0 2 -1 X1 = and x2 = -1 -2 4 0 projy(v) =
Please attempt all questions.
2. Use the polynomial inner product to find the projection of f(*) onto g(x). (a) f(x) = -12 -1, 9(20) = ? (b) f(x) = 2x2, g(x) = 2+1 (C) f(c) = -1-1, g(x) = r2 +3 3. Use the continuous function on the interval [0,1) inner product to find the projection of f(x) onto g(2). (Feel free to use an integral calculator. I use wolfram alpha. Just make sure to type the problem in carefully)....
Hi,
could you post solutions to the following questions. Thanks.
2. (a) Let V be a vector space on R. Give the definition of a subspace W of V 2% (b) For each of the following subsets of IR3 state whether they are subepaces of R3 or not by clearly explaining your answer. 2% 2% (c) Consider the map F : R2 → R3 defined by for any z = (zi,Z2) E R2. 3% 3% 3% 3% i. Show that...
Please attempt both questions
3. Use the continuous function on the interval (0,1) inner product to find the projection of f(x) onto g(x). (Feel free to use an integral calculator. I use wolfram alpha. Just make sure to type the problem in carefully). (a) f(x) = -22 - 1, g(x) = -2 (b) f(x) = 2r?, g(x) = 2+1 (e) f(x)=-1-1, g(x) = x2 +3 4. Consider 3-space with the dot product. Your subspace S will be the plane z...
(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...
Section 5.5 Orthonormal Sets: Problem 6 Previous Problem Problem List Next Problem 1 (1 point) Use the inner product < f, g >= . f(x)g(x)dx in the vector space C°[0, 1] to find the orthogonal projection of f(x) = 6x2 + 1 onto the subspace V spanned by g(x) = x - and h(x) = 1. projy(f) =
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