5. (a) Let a, b, ce R3. If det(a, b, c) # 0, prove that a, b and c are non-zero. (b) Prove that x x (y x z) = (x z)y - (x y)z for all x, y, z ER. %3D

Q: 1 Let f (x,y) =In Then f (1, – 1) =... 3x2+4y3 XX

A:

Q: az xdz + Y- = xy+z. a) If z = xy - xei , show that x- ду

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Q3: Prove that Σ(y₁ - y) = 0 AND Σfi(y₁ - y) = 0

A: The question is about proving given equation. To prove : ∑ ( yi - y¯ ) = 0∑ fi ( yi - y¯ ) = 0

Q: Which of the following is homogenous of smallest degree? (A x+y B) In x - In y x4+y4 x-y D Vx-y

A:

Q: 1. Let f(x, y) = In(x - y) then at the point (4,1), fryis equal to: %3D -1/9 O 1/7 1/9

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Let f(x, y) = xcosy- y e*y. fry at (1,0)is equal to: -5 3 -1

A:

Q: 6. Prove that for x > -1 then Vn E N, (1 + x)" >1+ nx .

A:

Q: A large but sparsely populated county has two small hospitals, one at the south end of the county…

A: "Since you have posted a question with multiple subparts, we will solve first 3 sub-parts for you.…

Q: (e) If f(x) is reducible over Q then f(x +a) : a E Z is reducible over Q.

A:

Q: 2. If z = x° In 2.xy, find at 1,-

A:

Q: 2. Show that 4=x i+y°j+:'k is irotational.

A:

Q: 1. A function f(x, y) is homogeneous of degree 7 in x and y if and only if, 2. The function f(x, y)=…

A: We have to find degree of homogeneous function

Q: 1. re (x, y, z) x). Ly). (z}} - *(*. y, z) . (x)S(x), ly), (z]} (x)E (x, y, z}

A: If x is element then it belong to set And {x} it will be subset of set

Q: 3[ .. :] Let X and Y have joint pdf S 2x, 0<x< 1,0 <y<1 0, f(x,y) = otherwise Find the covariance of…

A: Cov(X,Y)= ?

Q: 3. If f(x, y, z)= In xyz te(3.0²), find f,,f, and f-· 4

A:

Q: 7) Suppose w=rt+rs' and r= tan-' (2x² +3y), s=x²y' +3y and t = x²y² .Use the chain rule (from…

A: Given w=r2t+rs3r=tan−1(2x2+3y)s=x2y3+3yt=x2y2

Q: 1. Let g(x, y) = ev* /x. Evaluate gry and gyæ.

A:

Q: -2 Let f(t,y) = y + 3t?e'. Then f satisfies a Lipschitz condition in y with L = 2, given that 1<t<2.…

A:

Q: -ALef xe Rbe Such thad Xn→x, show that Yn = xi %3D 4 X.

A:

Q: Let f(x, y, z) = In(x² + z) + y²e®%. Find fzym. Zyx•

A:

Q: 6. Find the Wronskian for the set of functions {e¬x, xe¯*, (x + 1)e¬*}.

A:

Q: 8. Given for C[0,1] the inner-product function (f,g)=[f(x)g(x)dx , find ||f|| if f(x) = x+1.

A:

Q: Let z(x, y) = xe* + sin xy + y - In 2 then a a) -In 2-2 b) In 2-2 2 c) 2 (²-1) d) - 2 (²+1)

A:

Q: Find

A: Solution is here

Q: Suppose that a) [15x²y; 0<x<y<1 f(x, y) = { 0; otherwise. Compute E(Xy), Var(X) and Var(Y). b)…

A:

Q: Suppose that a) b) f(x, y) = [15x²y; 0<x<y<1 0; otherwise. Compute E(X | y), Var(X) and Var(Y).…

A:

Q: Which of the following is homogenous of smallest degree? x4+y4 A x-y B Vx-y x-y x+y D In x – In y

A:

Q: ronskian of the DE : xp(x)y' + 3y = 0 = er² et? et?

A:

Q: 4. Let z = x2 + y³, x = 2st, y = s - t2, s = u", and t = u sin w. Compute for Oz ду and дw ди

A: Let z=x2+y3, x=2st, y=s-t2, s=uw, and t=u sin w.To compute for ∂z∂w and ∂y∂u.

Q: 9 Give with an not example of T: W≤X →Y, to XT Ext. .R. boundedag. - keše bes

A: Please find the solution innext step this is an non-example of Tietze extension theorem in Topology.

Q: (x, y, z) = VI - xVE – y. (x, y) In(1-x) In(z+y). (х, у). (x, y) = D. (x, y) = VT – x + y². /1 - x +…

A:

Q: Q/Use Definitien 13.4-1 +o prove that f(x,r}>x+y' is difterentialeat (o,0).

A: Given function is  fx,y=x2+y2

Q: 3) Calculate Wronskian and evaluate for which values a, b, c e R the following sets of functions are…

A:

Q: dz Find if yz – In z = x + y ax

A: To find the partial derivative of z of yz-ln z=x+y with respect x, differentiate yz-ln z=x+y, while…

Q: Let X,X, X be i.i.d. with the following PMF. ...... 25 0.6 ; k = 1 Pk)= 1 0.4 ; k = -1 and let Y =…

A: Answer: For the given data,

Q: 2): Consider the DE y" – y" – 6y = 0 -

A: Follow the procedure given below.

Q: дz (B)If Z = f(x, y), x= s² - t², y = 2st. Prove that s მs 2 (s² + t²) of əx

A:

Q: Let X and Y have the joint p. d. f . sx+y if 0<x, y < 1 elsewher f (x, y) = %3D The covariance…

A: Given X and Y have the joint p.d.f. fx,y=x+y  if  0&lt;x,y&lt;1    0          elsewhere

Q: 1 3. Integrate the function f (x, y) = over the region bounded by x-axis, line x = 7, and the curve…

A:

Q: Let Xi- N co,1) and n=2 auel T= Xi+ Xz Show that Tis a %3D Sufficiency Stabisuic Statistic.

A:

Q: 10- If f(u, v, w) is differentiable and u = x - y, v = y - z, and w = z - x, show that fe fe fe = 0.…

A:

Q: 3. If f(x,y,z)= In 4 xyz Ite t3y:²s²) , find f,,f, and f..

A: Given that: f(x,y,z)=lnxyz4+e-(3xy2z2)

Q: 1 Let f (x,y)=In . Then f „(1, – 1) =...... 3x²+4y3 XX

A:

Q: If f(x) - g(x) = 1, then f and g have the same antiderivative. %3D O True False

A:

Q: Find fCx) if flo)=0 and the tanGat (k,F CX) has ine af Slore x(x+2) a

A: Given for the function F(x), F(0)=0 and tangent line to F(x) at x,F(x) has slope xx2+23.

Q: If f(x,y,z)=z In(x²ycosz), then fz is O 2z X OZ y O2z y O In(x²ycosz) - ztanz <|N

A: This question is related to partial differentiation, We will solve it using given information.

Q: Suppose / (s) - (÷)*" valuate: Js(x) dr +C 3- In (5)

A: Given      f(x) = 1512-3x

Q: Find f, and f and evaluate each at the given point. F(x, y) = e*y?, (In 4, 2) f(x, y) f,(x, y) =…

A:

Q: Suppose that a) b) f(x, y) = [15x²y; 0<x<y<l 0; 0; otherwise. Compute E(X|y), Var(X) and Var(Y).…

A:

Q: 16.1. Use an antiderivative to show that for every extending from a point 21 to a point 22 2" dz =…

A: