(5) 3 IS IR²³ = Span { 1²₁, 0₂, 03 бран Е Is where &₁ = (1, 0, 1) ů √ 2 = (-1,1,2) √ ₁ = (0₂1,0) 3 ?

Q: 1. The vector X = k is a solution of x - (: -)x-G) 8, X' 2 for k = Enter only the value of k.

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Q: 1. Let T = [-2 1 0 5], 5 1 1 0 A = [¦ ¦] ·--[¦ ¦ ). -- [¦ ¦ ¦]. - -[] [16], B = = [1 2] C = D = 0 3…

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Q: If U(x,y)=In(x²-y³) then Ux+Uy= ... XX

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Q: 2) vting daplace toansfóöre, Solve x" Zt)+4x'Lt)+3=(4) uing = 10 gint yeren that xco) = -3t Ans: ILt…

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Q: The equations ry? + 5zzcos(u) + ye" = 10 and zyz + ze" - 4u = 12 are solved for u and v as functions…

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Q: The equations xy² + 8xzcos(u) + ye" = 16 and xyz + xev – 9u?v² = 27 are solved for u and v as…

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Q: Please solve number 3

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Q: #2. Define the operators 33/32 = 1/2 (3x +²y), 32= 2 (x-7) = u(x, y) +iv(x, y), show that (af (3) =…

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Q: 5. Let z1 = a1 + b;i and z2 = az + bzi. (a) Find Im[z,Zz + (Z)? – 2,7 ]. (b) Prove that (z)² = z,² .

A: Rational Numbers: All the numbers which can be written in the form of pq. Here, p and q are integers…

Q: Solue the guen equaitions %3D

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Q: b) Find all the analytic functions for which Rez = Im f(z)

A: b) A function f(z) is said to be an analytic function at any point z=a if f(z) is differentiable not…

Q: 9) Solve: (x + y)dy-(z-y)dx=0 a) x² + y² = C b) z² + 2xy + y² = C c) z²-2ry+y²=C d) z²-2ry-y²=C

A: We need to solve D.E.

Q: answer each question by true or false and explain 1) L{t * e³t} = L{te³t} 2) L-¹{L{t* et}} = t * e³t

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Q: a) Use the Euler formula, e¹⁰ (cos(0) + i sin(0))" = cos(n) + i sin(n). b) Suppose y(t) = e-2t eit…

A: In this question, we will find the solution to the given problem.

Q: 2 [11]₁v=₁-1²] W u Compute: u.v= u. W = w u · (v + w) = u.v+u. W =

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Q: let it be 2= f(x,y) and Y=tan' () and X = === In (r²+5²) Prove that fxx+fxy= (y² + S) (fr+fso)

A: We have to prove

Q: b. -2åx + 3d, - åz 2. If E = -xả, + yåy V/m, find the work involved in moving a unit positive charge…

A: We can solve using given information and calculate the work done

Q: The indicial equation of (-1) y"+ (-1)y'+2u 0 at r=1 is: (A) + 2r +1=0 (B) r1 2r = 0 (C) r-r= 0 (D)…

A: Given differential equation is (x-1)2y"+(x3-1)y'+2y = 0

Q: a) If L-{F(s)} = f(t) and L-1{G(s)} = g(t), and if a and B are constants, then L-1{aF(s) + BG(s)} =…

A: If L[f(t)]=F(s), then f(t) is called the inverse Laplace transform of F(s). That is; f(t)=L-1[F(s)]

Q: 16)- Consider the quadrature formula 6 | f(x)dx = Af (-6) + Bf(6) -6 If the degree of precession is…

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Q: a3 f 2- Find the third derivative for for f (x, y) = sin əx3 -2sin?cos()+2 sin) sin By'sini )+2…

A: The given function isf(x, y)=sinxy

Q: B) Find (블)x,()'(일), Prthe Pte 2- w= x?+y-2 +sin z 3. w:x+y+2", ysinz+ z sin so

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

Q: 1. (r - x) + (-2r + 3x) 2. (-y + 3) - (v - 2) 3. (-3a* + 4 + 2a') -(2 + Sa - a) 4. -(6 - b + 4b')…

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Q: 7. Evaluate * (D5 – 3D¹ + 8D³ + 16D² – 9D – 13)y = 0 y = (C₁+C₂x)e¯x + Сze* +C₁е²x cos3x +C5e²x…

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Q: 1. Найдите первообразную функции a) y = 52+2 Vx б) y = 3 sin 1-2x 3

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Q: Given z(x, y) =In(2xy) where x(u,v)= e" cos(4v) and y(u,v)=e" sin(4v). Find ди 1 cos (4r)+-sin(4v)…

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Q: Find a formula for u(x, t) that solves Ихх сис u(x, 0) = and show that (a) \4(x, t) 51

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Q: 24. For a constant vector E, find the constant k such that V(FE) = KË: C) km-l D) - A)k-0 B)k-1 E)…

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Q: What is the equation of the tangent plane to the graph of 3x²+4y²-2²=3 at the point (1,1,2) ? 03 1…

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Q: The equations ry² + 8xzcos(u) + ye® = 16 and x³yz + xe" – 5u²v² = 15 are solved for u and v as…

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