Say that E = Ãek™, where the components of A and k are real and constant, i.e. they aren't imaginary and don't depend on x, y, and z. Is it true that V · Ē = ik · Ē?

Q: Show that in R2, (a) i·i = j·j = 1; (b) i·j = 0.

A: a)- To show that i·i=j·j=1 As, the dot product is represented by: a·b=abcosθ Using, it we have:…

Q: Find the solution formula of u(x, y) for Uxx + Uyy = 0, uy(2,0)=0, u(x,b)=0, u(0, y) = 0, u(a, y) =…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Express ∂w/∂r and ∂w/∂s in terms of r and s if w = x2 + y2, x = r - s, y = r + s.

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Q: Let A = {a1, a2, a3} and D = {d1,d2, d3} || be bases for V, and let P = [[d]]A [d2]a [d3]a]. Which…

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Q: Let fxy (x, y) = 6 (x – y) , 0 < y < x < 1. If E (X) = , E (Y) = Cov (X, Y) = then %3D

A: Given,fXY(x,y)=6(x-y) ; 0&lt;y&lt;x&lt;1E(X)=34E(Y)=14

Q: following (a) E(X) and E(Y) (b) Cov(X, Y) (c) Are X and Y independent? Justify your answer.

A: Solution

Q: Use Cramer's rule to solve for y without solving for x, z, and w. y + 5x + 3y 5х + z + w = -7 z + =…

A: Given:

Q: = + E (0 < x < L,0 < t <ox) L Ot u (0, t) %3D 0, и(L,t) %3 0, и(х,0) — А, и (т,0) %3D0.

A: Given - ∂2u∂x2 = ∂2u∂t2 + πL∂u∂t , u0, t = 0 , uL, t = 0 , ux, 0 = A , ∂∂tux, 0 = 0 , 0 &lt; x &lt;…

Q: こ= (t)} () て= () %3D - (^),J %3D てんn ZトXC

A: →∫eax+bdx = eax+ba + C, where 'C' is the constant of integration.→∫xndx = xn+1n+1 + C

Q: Let A = {a1, a2, a3} and D = {d1,d2, d3} be bases for V, and let P = [ [d¡]a [d2]A_ [dz]a ]. Which…

A: We will use the following theorem to find the correct option.  "Let B=b1, b2, b3,...,bn and C=c1,…

Q: Use Cramer's rule to solve for y without solving for the un- knowns x, z, and w. 4x + y+ z + w= 6 .…

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Q: Let u(x, t) be the solution of n. и = xt, -00 0, .2 ди (x, 0) = 0, –00 < x < ∞. u (х, 0) - %3| -…

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Q: Let u = f(r, s),r = x + at, s = y + bt, where x, y,t are independent variables and, a and b are…

A: We have to show given identity: Given u = f(r, s) r= x+ at s = y+ bt where x, y, t are independent…

Q: Solve the Auxiliary DE 75. и"" + u" — 2и 3D 0

A: Note: - “Since you have asked multiple question, we will solve the first question for you. If you…

Q: of af and Let f(x, y, A) = xy + A(5 – x – y). Find· ax' əy` af

A: f(x,y,λ)=xy+5λ-λx-λy .....(1) Differentiating (1) partially with respect to x, ∂f∂x=(1)y+0-λ-0…

Q: Let z= I= 2e", and y = 3 ln v. Find in terms of u and v.

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Q: (b) Use Cramer's rule to solve for y without solving for the unknowns x, z, and w. 4x+ y+ z+ w= 6…

A: Crammers rule is applicable to a system that have non zero determinant for the coefficient matrix.…

Q: Use Cramer's rule to solve for y without solving for x, z, and w. 4x + y w = 3 5x + 2y 4 4x 2 y 5z +…

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Q: U + 2ru, =0 IER, t> 0, u(x,0) =e=.

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: Solve the following aw dw aw. Q1) w(x,y, z) = xy²z³ + esin(x*y²z) + x² – y³ + z – 7 find ( дх ду az

A: Here x,y and z are independent variables and w is the dependent variable that depends on x,y and z

Q: Given u(x, t) = t°e¯ï, compute:

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Q: By substituion, u=(y/x) in equation xy'=(x2+y2)1/2 we have u'*x+u=(?)1/2. a) u b) u2 c) 1 d) u3…

A: Substitution in differential equation

Q: Find ∂z / ∂v using the chain rule if z = sin(x/y), x = ln(u), and y = v. Put the answer in terms of…

A: Firstly, we find partial derivative of z with respect to x and y, partial derivative of x with…

Q: Use Cramer's rule to solve for y without solving for x, z, and w. 4x + y + z + = 7 5x + 3y z + 8 W…

A: Let's find.

Q: A = (C = { z = x+yi : x, y E R, i² = -1},+), (a+bi)+(c+di) = (a+c)+(b+d)i • B = iR = { iy : y E R }

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Q: Use Cramer's rule to solve for y without solving for x, z, and w. 3х + y + z + = -6 W 2x + 2y z + =…

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Q: Let D, E ⊂ C be starshaped w.r.t the same z∗ ∈ D ∩ E. Show that D ∪ E, D ∩ E are starshaped

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Q: Which of the following are first order linear aiterential equations? F. = y – 3y

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Q: For which values of z is w =1/(z – i), defined? For these values obtain u and v and evaluate w when…

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Q: Suppose u=, v=x +y and w w(u.v): a) Express W and W, in terms of W. . X and y b) Calculate xW, +yw,…

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Q: Use Cramer's rule to solve for x, y and Z 2х + у — 3z %3D 0 | 4х + 5y + Z %3D 4 %3D

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Q: Solve for x, where u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). 2x − u + 3v + w = 0

A: Given u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). And 2x-u+3v+w=0 Plugging the values,…

Q: Use Cramer's rule to solve for y without solving for the un- knowns x, z, and w. 4x + y + z+ w= 6 3x…

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Q: If u = ₁+₂y+z, where a₁, A2, A3 al constants and J²u J²u J²u น a +a+a = 1. Show that + + = U. მ2 მყ2…

A: This question is based on Partial diffrentiation.

Q: Use Cramer's rule to solve for y without solving for x, z, and w. 5 x + y + z + W = -7 5x + 3y - z +…

A: Here we have to use cramer rule for solving the system of linear equations

Q: Find a and b such that v au + bw, where where u (1, 2) and w - v- (0, 6)

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Q: Determine the real number \( \alpha \) u x v and î are orthogonal, where ù = 3î + ĵ– 5k and v = 4î –…

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Q: Solve for w, where u = (1, −1, 0, 1) and v = (0, 2, 3, −1). 1/2w = 2u + 3v

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Q: Calculate A and B so that t B %3D 1+1 (1-z²)

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Q: Show that u = (a, b) and v = (e, d) in K? are linearly dependent if and only if ad – be = 0.

A: Solved below

Q: Q) Verify that (bx с) %3D b.(с х а) — с. (а x b) if a %34i — 3ј +6k , b- 5i +4j — 3k, с %3 4i +6j +3…

A: Given the three vectors

Q: Let P, Q, and R be the points at 1 on the x-axis, 2 on the y-axis, and 3 on the z-axis,…

A: Let O is the initial point (0, 0, 0) and the vector OP, OQ and OR vector can be represented as:

Q: (ii) e*u + e'u„ = u XX yy

A:

Q: Find those constants a, b, c, d such that f(z) = ax² + bxy + y² + i(x² + cxy + dy?)

A: The given function is : fz=ax2+bxy+y2+i(x2+cxy+dy2)

Q: Solve for x, where u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). 3x + 2u − v + 2w = 0

A: The given vectors are Let the vector x be

Q: (A) g(z|y) = h(y|x)fy(y)/f=(x) (B) g(r|y) = h(y|x)f=(x)/fy(y) (C) g(r|y) = h(r|y)f=(x)/fy(y)

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Q: Show that in R2 ,(a) i · i = j · j = 1;           (b) i · j = 0.

A: We have to show that In R2 (a)       i · i = j · j = 1   (b)      i · j = 0

Q: O eiz dz < z2 – i e2 , 3 - z(t) = 2e", t e [0,27]. true False

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Q: Let a A =| d e f h i and 2a 2b 2с B = 2d 2e 2f i Given that det(A)=1/12, what is det( B-)? Answer:

A: Other