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

Q: y" - Зу' — 4у — 0

A: Given differential equation is y" -3y' -4y=0

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

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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: If =x+3y-z,=4xyz, w=22 -xy evabuate d(u, v,w)/ (, 2). at (1-,0).

A: We have to first find all partial derivatives.

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: then -A U= 4 5 and uTu · [

A: The given matrix

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: Find the cofactor of the element a13- -2 -1 0 5 4 2 3 5 O A. 3 О В. 19 ОС. -3 O D. 14 3.

A: Given a square matrix, the cofactor of aij is denoted by Aij=(−1) ^(i+j)M where Mij s the minor of…

Q: 3) u = y f( ise XU, + yu, t zu. = ?

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Q: Show that day) = So, x** 0₁ X=Y. defines a metric on X₂

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Q: Find ||uLy|| in Figure u= (3, 5) = (8, 2) P. FIGURE

A: v=(8,2) u=(3,5) uv=?

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: a2u a2u 2y дхду a²u )Find du where ax - - axây' ay? u = x3 - 2x2 + 2y3 – 6xy + y ax2

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Q: Vx3y P(x,y) is equivalent to 3x Vy P(x,y). True O False

A: Given that ∀x∃y Px,y is equivalent to ∃x∀y Px,y. To find that the statement is true or false.…

Q: 5(u-) du 2. 2

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Q: 2. For x 2 0, which equation is false? 3, 2 (x) = V3 А. X2 %3D B. (x³) = Vx3 c. (x) = Vx3 ( = С. X2…

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Q: swer C. If AB-5. -? IfC -A +B, and F =A-B, then C-F-? WO

A: It is given that AB→=5. The given figure is a cuboid. Thus, AB→=CD→=FE→. Since AB→=5, FE→=5.

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

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Q: Suppose that u × v = ⟨1,0,4⟩. Find (2u−3v) × v.

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Q: If u = eª₁x+₂y+a, where a₁, a2, a3 are constants and 2² u J² u 2² u + = U. a² + a² + a² = 1. Show…

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Q: 1-3у 2у - Зу? 1.

A: Given: ∫1-3y2y-3y2dy

Q: Let g(x, y) = 3.2³-6-2²-5.y2 +1. a. ag Show/hide

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Q: dw и and if w = x³ + In (²) dv E) + y, x = u² –" + 5 and Find - ди y = 3v + 5u and point…

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Q: Can u help me with this ( 17, 9 ) ( 17 , 2 ) M=y2 - y1 x2 - x1 M= 2-9 18 - 16 M= And can u help…

A: Given the points ( 17, 9 ) ( 17 , 2 ). We need to find the slope of the line passing through that…

Q: Find yp for y" + 5y' + 4y = -2x + 3 1- O Option 1 XIN 2 +8+ C

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Q: Consider the two following graphs and answer the following questions. a) Are G and H isomorphic?…

A: The graphs given are as follows:

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

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Q: In ADAT, mZD = 8x – 6, mLA 5z + 12, and m/T = 7x – 26. Find z and mZT. (Hint - Draw a picture…

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Q: Suppose a, = (1 -1 1 1) 5. a, = (1 0 1 0)" a, = (1 1 1 1)'a, = (3 2 3 0)" · Please find out whether…

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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: Suppose ū = (-4, 1) and ū = (0,4). Then: u+0= u - D= 0 - u= 4u= 4u – T0=

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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: If find az/au and az/av. дz/?u = Əz/dv= z = xe", x=u³v³, y=u³+v³₂ (In your answers, do not rewrite…

A: z=xeyx=u3-v3y=u3+v3from chain rule ∂z∂u=∂z∂x×∂x∂u+∂z∂y×∂y∂u

Q: Let a + 0. Assume that (5A – 3B) = I with | 1 2 3 A = 0 -4 -7 . Find ) 11 -1 the (2,3) entry of B.…

A: The given matrix is,A=1230-4-7011-1

Q: Kindly exhibit that xzxx+yzxy=y2zyy if z=xy+yln(xy)

A: The given data is: z=xy+ylnxy To prove: xzxx+yzxy=y2zyy