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1) Let F be the...
Exercise 1: (20pts) Let u1-11, 1, 1)T, u2-(1, 2, 2)T, u,-(2, 3, 4)T, ν,-(4,6,7)T, v2 =...
Exercise 1: (20pts) Let u1-11, 1, 1)T, u2-(1, 2, 2)T, u,-(2, 3, 4)T, ν,-(4,6,7)T, v2 = (0, 1,1)1 , V3 = ( ) (a) Find the transition matrix from fvi, v2, vs] to sui, u2, us] (b) If x 2vı +3v2 - 4vs, determine the coordinates of x with respect to fui, u2, us] 0,1,2
Hi, Can you help me with this one? Thanks? CIUI. U LUS de LE SUSTASUL. EL...
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Can you help me with this one? Thanks?
CIUI. U LUS de LE SUSTASUL. EL SALE UUTTUIUJ- Uin U2+U, NU 4. Let U = {fe P3 f(-r) + f(x) = 0 for every r}. Prove or disprove. (a) Ps= U P2 (b) Ps= U + P1 Lot n-1-2-10121 II Ful l - for a consider
1 -1.2 5 Uį = U2 = -3 1, U3 = 2 , 14 = 29...
1 -1.2 5 Uį = U2 = -3 1, U3 = 2 , 14 = 29 ( 7 Answer the following questions and give proper explanations. (a) Is {ui, U2, uz} a basis for R3? (b) Is {ui, U2, u4} a basis for R4? (c) Is {ui, U2, U3, U4, u; } a basis for R? (d) Is {ui, U2, U3, u} a basis for Rº?! (e) Are ui, u, and O linearly independent?! Problem 6. (15 points). Let A...
question starts at let. than one variable. Let f:R? → R3 be the function given by...
question starts at let.
than one variable. Let f:R? → R3 be the function given by f(x, y) = (cos(x3 - y2), sin(y2 – x), e3x2-x-2y). (a) Let P be a point in the domain of f. As we saw in class, for (x, y) near P, we have f(x, y) f(P) + (Dpf)(h), where h = (x, y) - P. The expression on the right hand side is called the linear approximation of f around P. Compute the linear...
CHANGING COORDINATES/BASIS Question 1. Let R be the triangle in R2 with vertices at (0,0), (-1,1),...
CHANGING COORDINATES/BASIS Question 1. Let R be the triangle in R2 with vertices at (0,0), (-1,1), and (1,1). Consider the following integral: 4(x y)e- dA. R Choose a substitution to new coordinates u and v that will simplify this integrand. Draw a sketch of both the region R and the image of the region in the u,v-plane. Evaluate the integral in the new coordinate system. Warning: No matter what strategy you use for this integral, it will require at least...
Problem 1: Let F(, y,) be a function given by F(, y, z) (r2+y)e. Let S be the surface in R given ...
Problem 1: Let F(, y,) be a function given by F(, y, z) (r2+y)e. Let S be the surface in R given by the equation Fr, y, 2) 2. (a) Find an equation of the tangent plane to the surface S at the point p(-1,1,0) (b)Find the directional derivative -1,1,0) of F(,y,2) in the direction of the unit vector u = (ui, t», t's) at the point p(-1,1,0) - In what direction is this derivative maximal? In what direction is...
Hi! Please help me with this question #1. Thank you so much! In each of Problems...
Hi! Please help me with this question #1.
Thank you so much!
In each of Problems 1-6, find the expansion of f(x) in the eigenfunctions of the given Sturm-Liouville prob- lem. Compare graphs of the function and the Nth par- tial sums of the series for the given N. Also use the convergence theorem to determine what this eigen- function expansion converges to on the relevant open interval. 1. y' + y = 0; y(0) = y(2) = 0 f(x)...
Please answer A, B, and C in full 2. Let f() € F[2] be a separable...
Please answer A, B, and C in full
2. Let f() € F[2] be a separable polynomial with roots {u1, ..., Un} contained in some splitting field K of f(x) over F. Define A= || (ui-u) = (ui - U2) (u - u3) ...(ui-un)(uz - u3) ..(un-1 - Un) EK. (a) (15 points) Consider GalpK < Sn by looking at its action on the set of roots for f(x). Show that if Te Galo K is a transposition then (A)...
Please show the detail, thank you! (1 point) (a) Let -4 -7 -2 -4 V1 =...
Please show the detail, thank you!
(1 point) (a) Let -4 -7 -2 -4 V1 = and V2 = 1 6 0 2 and let W = span{V1, V2}. Apply the Gram-Schmidt procedure to vi and V2 to find an orthogonal basis {uj, u2 } for W. uj = U2 = -13 2 (b) Consider the vector v = - Find V' E W such that || V – v' || is as small as possible. 15 8 V =...
Please be detailed in your answer. Thank you. 1. Let f g be measurable functions defined...
Please be detailed in your answer. Thank you.
1. Let f g be measurable functions defined on a measurable domain E. Let A, = {x € Elg(x) = 0}. It is clear that the domain of() is A . Prove the following: a. A, is a measurable set. b. (1) is a measurable function on Ap. Hint: Show that for every a € R, {xea |^)(x) < a} is m easureable. Start by proving that {x e Aol (6) (x)...
Exercise 1: (20pts) Let u1-11, 1, 1)T, u2-(1, 2, 2)T, u,-(2, 3, 4)T, ν,-(4,6,7)T, v2 = (0, 1,1)1 , V3 = ( ) (a) Find the transition matrix from fvi, v2, vs] to sui, u2, us] (b) If x 2vı +3v2 - 4vs, determine the coordinates of x with respect to fui, u2, us] 0,1,2
Hi,
Can you help me with this one? Thanks?
CIUI. U LUS de LE SUSTASUL. EL SALE UUTTUIUJ- Uin U2+U, NU 4. Let U = {fe P3 f(-r) + f(x) = 0 for every r}. Prove or disprove. (a) Ps= U P2 (b) Ps= U + P1 Lot n-1-2-10121 II Ful l - for a consider
1 -1.2 5 Uį = U2 = -3 1, U3 = 2 , 14 = 29 ( 7 Answer the following questions and give proper explanations. (a) Is {ui, U2, uz} a basis for R3? (b) Is {ui, U2, u4} a basis for R4? (c) Is {ui, U2, U3, U4, u; } a basis for R? (d) Is {ui, U2, U3, u} a basis for Rº?! (e) Are ui, u, and O linearly independent?! Problem 6. (15 points). Let A...
question starts at let.
than one variable. Let f:R? → R3 be the function given by f(x, y) = (cos(x3 - y2), sin(y2 – x), e3x2-x-2y). (a) Let P be a point in the domain of f. As we saw in class, for (x, y) near P, we have f(x, y) f(P) + (Dpf)(h), where h = (x, y) - P. The expression on the right hand side is called the linear approximation of f around P. Compute the linear...
CHANGING COORDINATES/BASIS Question 1. Let R be the triangle in R2 with vertices at (0,0), (-1,1), and (1,1). Consider the following integral: 4(x y)e- dA. R Choose a substitution to new coordinates u and v that will simplify this integrand. Draw a sketch of both the region R and the image of the region in the u,v-plane. Evaluate the integral in the new coordinate system. Warning: No matter what strategy you use for this integral, it will require at least...
Problem 1: Let F(, y,) be a function given by F(, y, z) (r2+y)e. Let S be the surface in R given by the equation Fr, y, 2) 2. (a) Find an equation of the tangent plane to the surface S at the point p(-1,1,0) (b)Find the directional derivative -1,1,0) of F(,y,2) in the direction of the unit vector u = (ui, t», t's) at the point p(-1,1,0) - In what direction is this derivative maximal? In what direction is...
Hi! Please help me with this question #1.
Thank you so much!
In each of Problems 1-6, find the expansion of f(x) in the eigenfunctions of the given Sturm-Liouville prob- lem. Compare graphs of the function and the Nth par- tial sums of the series for the given N. Also use the convergence theorem to determine what this eigen- function expansion converges to on the relevant open interval. 1. y' + y = 0; y(0) = y(2) = 0 f(x)...
Please answer A, B, and C in full
2. Let f() € F[2] be a separable polynomial with roots {u1, ..., Un} contained in some splitting field K of f(x) over F. Define A= || (ui-u) = (ui - U2) (u - u3) ...(ui-un)(uz - u3) ..(un-1 - Un) EK. (a) (15 points) Consider GalpK < Sn by looking at its action on the set of roots for f(x). Show that if Te Galo K is a transposition then (A)...
Please show the detail, thank you!
(1 point) (a) Let -4 -7 -2 -4 V1 = and V2 = 1 6 0 2 and let W = span{V1, V2}. Apply the Gram-Schmidt procedure to vi and V2 to find an orthogonal basis {uj, u2 } for W. uj = U2 = -13 2 (b) Consider the vector v = - Find V' E W such that || V – v' || is as small as possible. 15 8 V =...
Please be detailed in your answer. Thank you.
1. Let f g be measurable functions defined on a measurable domain E. Let A, = {x € Elg(x) = 0}. It is clear that the domain of() is A . Prove the following: a. A, is a measurable set. b. (1) is a measurable function on Ap. Hint: Show that for every a € R, {xea |^)(x) < a} is m easureable. Start by proving that {x e Aol (6) (x)...
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