Find an upper triangular U (not diagonal) with U2 = I which gives U = u- 1.

Q: Calculate F . dr, where C is the square of (1,1, 1), (–1,1, 1), (-1,–1,1) and (1,–1,1), with…

A: Let F→x,y,z=zex-yezi→+2cosy-xezj→+ex-xyezk→ and C is the square with vertices…

Q: Evaluate the integra ∮C -y3 dy + x3 dx for any closed path C.

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Q: 1. Find a non zero unit vecor ôî that is orthogonal to u= (1,2,1) and Uz= (2,5,4) in R³.

A: Let's find non zero unit vector.

Q: Find ôz|ðu and ôzlôv for z=4e* In(y), x=ln(ucos(v)), y=usin(v) at the point (u, v) = (2, 7 | 4).

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Q: Show f(x) = e and g(x) = xe linearly independent by finding its Wronskian.

A: Given: fx=exgx=xex The formula to obtain the Wronskian is Wx=f(x)g(x)f'(x)g'(x), where f(x) and g(x)…

Q: Find the work done by the force F = x²yi– xy²j along the paths shown from (1, 1) to (4, 2). (4, 2) a…

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Q: of the valve matix is consistant e an linear

A: Given augmented matrix is: -412h2-6-3 Let the variables be x, y. The above augmented matrix will…

Q: Use the Chain Rule to find ôz/ðs and ôz/ôt. z = tan(u/v), u = 9s + 8t, v = 8s – 9t as az at

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Q: = a + zy", z - w* + w, y I = uu" + w", y u+ ve fi az Find when u = 1, v 2. w=0 = %3D H.

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Q: Given that u. = = = , show that EE,(tB)ij = 0, where (tB)ij is the interaction effect in the…

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Q: Exercise 2.8. Verify that q eAt-d satisfies the "martingale property" %3D u-d Sug + Sa(1 – q) =…

A: Given,  q= erΔt - du - d Consider ,  su q + sd (1-q) = su erΔt - du-d +sd1-erΔt - du - d= su erΔt -…

Q: Compute u x v. (a) u = 2i + 3j+ 4k, v = -i+ 3j – k (b) u =i+ k, v = 2i + 3j – k (c) u =i-j+ 2k, v =…

A: Note: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts…

Q: b) Show that the implicit Trapezoidal method h Wi+1 = Wi +5 f (ti+1, Wi+1) + f(ti, w;), is…

A: The solution is given below in the next step:

Q: Find the Jacobian w/ respect to UVW X=U(3-v), Y= uv(3-w), Z=Uw

A: Our aim is to find the jacobian of x=u(3-v), y=uv(3-w) and z=uvw⇒x=3u-uv ,   y=3uv-uvw and…

Q: Exercise 4.3.8 Show that if A = E oiu;vf , then At = Ei=1 0,'v¿u

A: Given function is, A=∑σiuiviTi=1r As we know that, A+B+=A++B+ So, we can write the above equation…

Q: nto v. t of u orthogonal to v.

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Q: Use the Chain Rule to find dz/ðs and əz/ət. z = tan(u/v), u = 5s + 8t, v = 8s – 5t %3D az %3D as az…

A: We have to use chain rule to find the partial derivatives of z.

Q: Let C be the positively oriented square with vertices (0, 0), (3, 0), (3, 3), (0, 3). Use Green's…

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Q: Find over xlapping area two equatione also gemetrical nepresentahon 2. 4'+v?=n, u?+cV- vn)=1 whore n…

A: Given curves are,…

Q: Prove that f, uv v • dỉ = – §̟ vũu • dĩ

A: Whenever the force is conservative in nature the work done over the closed loop is always zero. i.e…

Q: t in 30 minute please duopoly with homogeneous goods. There ar

A: When there are only two firms in the industry, it is in their advantage to collude and set the price…

Q: tnd the kes reetor projection of anto r if

A: Given : u→=5i→+2j→ and v→=6i→-3j→

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (4,0,0), (0,3,0), and (0,0,2)

A: we have to find triple integral

Q: z dV, where E is the solid tetrahedron with vertices (0,0,0), (2,0,0), E Find (0,6,0), and (0,0,3)

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Q: Utu = c²uxx , u(0, t) = 0, u(1, t) = 0, u(x,0) = 0 U¿(x,0) = x² – 2x, 00 t> 0 t > 0 0sx<1.

A: Given P.D.E

Q: Let A = LU, where L is lower triangular with 1’son the diagonal and U is upper triangular. How many…

A: Given: Let A = LU, where L is lower triangular with 1’s on the diagonal and U is upper triangular.…

Q: of the b) nd y- Fons c) with point.

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Q: Given the bases B = {u1,u2} and B'= {u'1, u'2} for R, where and The transition mat rix P8-B from B…

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Q: Use the Chain Rule to find ðz/ðs and az/ðt. Z = tan(u/v), u = 8s + 9t, V = 9s – 8t %3D az ds az at

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Q: Find up +Uy given that u (x,Y)s. (x,x)s

A: Given that ux, y=tanx3+mx2y2+my4m-x2-y2 To find ux+uy we follow the following steps calculate…

Q: Q2:show that the force Fexyzi-x4z'k is Conservative. ?

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Q: fx) =x+x, aニー %3D LCx) = ? %3D

A: Our objective is to find the linearization L(x) at x=a.

Q: Use the Chain Rule to find ôz/əs and əz/ðt. z = tan(u/v), u = 4s + 7t, v = 7s – 4t Əz as az II

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Q: Find the surfaces on which the function u = 2 (x2 + y²)/z is constar

A: Since u is a constant so, x2+y2z=4a , where a is an arbitrary constant.

Q: 8. Evaluate the double integral // ydrdy where T is the triangle with vertices (0,-1), (0,5), (4,…

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Q: Evaluate the line integral x²z ds, where C is the line segment from (0,6, 2) to (8, 5, 1).

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Q: 4. let f(x, y) = x² – xy + y² – y. find the direction u and Duf at Po(1,–1) for which Duf is the…

A: Given:- f(x, y) = x2 -xy+y2 -y To find:- Direction u and Du f at point p0 (1, -1) for which Du f is…

Q: Use the Chain Rule to find az/ds and az/ôt. z = tan(u/v), u = 3s + 6t, v = 6s - 3t az as az at II

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Q: $ ((x,y) (E,6) )e product Prove 2 xt + 3yt on e?. Gompute inner IL(,2), where the norm i's…

A: We have to prove that f( (x, y) , (t, t) ) = 2xt + 3yt is an inner product on R2 . 1.) &lt; ( 0, 0 )…

Q: Q1- Determine the coordinates of the centroid of the area.: (1, 1)

A: We need to find the x coordinate and y coordinate of the shaded region which is bounded by two…

Q: Evaluate the double integral. 6y? dA, D is the triangular region with vertices (0, 1), (1, 2), (4,…

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Q: Find ff -6xydA over the D triangular region D with vertices (0,0) (2, 0), (0, 4)

A: problem is related to double integration

Q: Verify the chain rule for jacobian, if y2 u = x + , v = * y2 %3D

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Q: What solid is formed when this net is folded? A C D

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Q: Use the Chain Rule to find ôz/ds and ôz/ðt. z = tan(u/v), u = 5s + 9t, V = 9s – 5t az as az at

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Q: (f) Find the length of the projection of i onto ū.

A: Given