1. Suppose that (R x R, +,.) is a field where (x, y) + (z, w) = (x + z, y + w) and (x, y). (z, w) = (xz – yw, xw + yz). Then (1,2)-1 (a) (2,1) (b) (;,-) (e) -) (d) No Choice

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A: Given: Tx,y→x+2, y To determine: T2x,y→?,?

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Q: Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the following applies.…

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Q: (a) Find the constants A, B, C, and D that satisfy 1 1 1+ (w/o)² 1 + ((z-w)/7)2 Aw B Cw D 1+ (w/o)²…

A: Use partial fractions

Q: z = f(st - 3, s2 +t) and fi(-1,9) = 3, f2(-1,9) = 7, fu(-1,9) = f12(-1,9) = f21(-1,9) = f2(-1,9) =…

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Q: If F(x, y, z) = (x²z, –2xz, yz), then curl F(6, –3, 1) equals %3D O (12, 39, –5) O (9,34, 2) O (13,…

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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: (5). If A, B and A+B are each non-singular and the products are conformable, prove that (a). A(A +…

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Q: Suppose that (Q x Q, +,.) is a ficld where (x, y) + (z,w) (x+z,y + w) and (x, y). (z, w) (xz +2yw,…

A: I have find identity of the field and then inverse

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

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Q: If f(z) = z² − (z)² + zz, calculate the following: a) u(x, y) and v (x, y) b) u(-10,-5) and…

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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: 2x (x-6) 3.) y = (x-3)3 required:a) yand y"

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Q: Suppose (B - C) D = 0, where B & C are m x n matricies and D is invertible. Show that B = C.

A: Given that  (B-C)D =0 here B and C are m×n matrices

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: Ay l Ory"- 8y/ (ry + y) O zyy"=/ (ry + 7y) O ry" - / (8zyy) O zy" =/ (zy - 8y)

A: We will find out the required value.

Q: Let Compute дw -(-2,-2) = -(-2,-2) = მs дw St W = 2xy - 2yz + 3xz, x = st, y = est, z = t² =

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Q: + Bz³) ûx + y)ûz

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Q: In(z,) + In(-v3 – 1) = In(2) +i %3D

A: Answer

Q: Let W(s, t) = F(u(s, t), v(s, t)) where u(1,0) = -2, u, (1, 0) = 8, ut(1,0) = -4 v(1,0) = -3, v.…

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Q: Prove if X,Z, y > 0 xy (3x +2y – 4z)+ yz(y+3z – 4x)+ xz(x+2z –- 4y)>0 then

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Q: 6) Show that (2xy, 2yz + x², y²) is conservative.

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