12 3. If u lx + my, v = mx-ly, show that ди 4 + m

Q: 2) Show that 2m +1 m P(x) m +1 -xP (x) m+1 (x)F

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Q: 1) Linearize: 3x arourd 天=l %3D

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Q: If A = 2 4 and B find: (а) АВ (b) А + B" (с) 2A' - В

A: Topic:- matrix algebra  Note:- as per our guideline if more than three subparts than  only first…

Q: Q4. Let flW=( Gué-4u-7) (4ax4 -8x#+15) Find tle regueetad closiuadtiul (10)

A: Given,

Q: If U = xz - x²2y + y²z², evaluate div grad U O2y + 2z²+2y² O -2y + 2z²-2y² O2y-2z²+2y² O2y + 2z²-2y²

A: I have given the answer in the next step. Hope you understand that

Q: 5) U₂ = 5 Uxx t U(0,€) = 2 U(3,4)=-1 U(x,0) = -x

A:

Q: If r(x, y,z) = (x² + y² + z²)!/2, find a²f a²f əx²'əy² ' a²f , аnd дхду

A:

Q: -If u = x2 tan-1 २|४ y = - y² tan-1 x 22u дхду x² что - у² + J²u u ә2u u дхду дудх L ala 2

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Q: 4. (5pts) Determine if the columns of 3 -2 5 -6 -1 A -6 0 3 4 7 span R'.

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Q: 23) -4V192X 25) -4V216xy'z

A: Given query is to simplify the expression.

Q: Suppose f(x, y, z) = xyz + 2xy + 2² · Compute the following values -(2,8₁16) - (-2,-8, 16) (1,-1,0)…

A: We have to find functional value.

Q: х — у—1 3y – 3x – 3y (1) = 1 у (1) %3D 1

A:

Q: əz əz 1. Let z = x² + y³, x = 2st and y = s − t². Compute for and əx Ət

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Q: 4. If w = x²y + y²z + xz², show that дw Әх дw дw дz = (x + y + z)2.

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Q: 4- compute dw dw дх' ду at the point (-2,3) if w = (2x + 3y - 1) ²

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Q: Compute the orthogonal projection of u onto v. Use the square root symbol '' where needed to give an…

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Q: Find r, s, and t so that (a) z = 1 2 x, (b) z + u = x, (c) z − x = y.

A: Given  And z+u=x and z-x=y. We need to find the value of r , s and t.

Q: 13. 2 [3] and u = [4] vectors, one in Span {u} and one orthogonal to u. Let y = . Write y as the sum…

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Q: 5) The equations r² + y²s + yt² - 13 and y² + x²s + rt² = 9 define s and t as implicit Əs functions…

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Q: Find J2z Әх у of z = x3 + 5x² у + 6

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Q: 6. Suppose that u₁ and u₂ are vectors with ||u₁||| = 2 and ||u₂|| = 3. You are also given that u₁ ·…

A: Given that  and  are vectors such that .Given that  and  for .We need to find  for .We need to…

Q: Suppose [V]s₁ =2]. If B₁ = { [2] [3]} ² and B₂ and B₂ = { [ ₁ ] [ 3 ] } find [v] [V] B₂ = =

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Q: 5. For which value of x do the following vectors form a linearly dependent set in ¹ X₂ G

A:

Q: 4.4. Suppose that u = (1,3) and v = (3, 1). (a) Sketch the points tu + žv, žu +v, and žu + jv. (b)…

A: Solution: Given u=1,3 and v=3,1

Q: [: ] c- [ ? 3 A = B = C = - 4 - 2 1 1- Compute the following а. (В — С)" b. 2BT – 3CT c. (D – 2A")"…

A: Given: A=120-170     B=134-1    C=1012    D=12-1102

Q: f of If dx + In(7y), what is ? - дхду Select one: 1 7. а. дхду y y b. дхду - y + 7e?y С. дхду 1+e7y…

A: Option E is correct.  Make x constant

Q: 1. If R=x²y i-2y²zj + xy²z²k, find a²R at the point (1, -2, 1).

A: