7. Let V={(x,y) x,y € R}. Suppose addition and scalar multiplication are defined using the following non-standard rules where c is any real number. (x,y)+(x₂.₂)-(x₂-x₂.0) c(x,y)=(-x,,Scy,) a. Find the result of (3,-2) + (-4,-3) under the above operations. b. Find the result of -3(2,-4) under the above operations. c. Show that V, with respect to these operations of addition and scalar multiplication, is not a vector space by showing that one of the vector space axioms does not hold. Clearly identify the axiom you have chosen.

Q: Find curl (5z i + 6x j + 9y k). curl(5z i + 6x j + 9y k) = ( i )i + ( i )j + ( i )k

A: Given: To obtain the curl (5z i+6x j+9y k)That is to find: ∇×Fwhere here F=5z i+6x j+9y k

Q: Find A and B such that 2x-1/(x+1)(3x+2) = A/x+1 + B/3x+2

A:

Q: Evaluate the commutators of the operators (a) d/dx and 1/x, (b)d/dx and x2.

A: Given:  a)  ddx and 1x b) ddxand x2 To Find: Commutator of the operators

Q: Show that Y1 = X1/X2 and Y2 = X1 + X2 are independent and that Y2 isχ2(r1 + r2).

A: Given Y1=X1X2Y2=X1+X2

Q: Let_Z1 = 3 + i and Z2 = 5 + 2 i . Find 2 Z1 /( Z1 - Z2) - (14/5)-2 i O (14/5) + 2i O - (14 / 5) + (…

A: Topic = Complex number

Q: 4x – 7y x - 2y Add: х — Зу - 3 Зу — х'

A: Given: 4x-7yx-3y+x-2y3y-x For adding given expression, we take L.C.M. and simplify it

Q: If z = 1-j3,Z2=-2+j5 and Z=-3- j4, determine in a + jb form: (a) ZZ (b) (c) Zi + Zz (d) Z,ZZ

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: xx X1+iy,=X2+iy20 2 X =X y= OךX

A: In the given question we have to choose the correct option from the given options  Concept: two…

Q: Calculate Duf (2₁-4,1) in the direction of 9 = 2₁ +2²₁ +3k for the function f(x, y, z) = x² +…

A:

Q: Differentiate y = xV A. 2Vx (2+In x) В. (2+In x) VX C. 2vx 2V (2 – In x) | D. 2V (2 + In x)

A:

Q: Find the values of x and y for which (x + y, 0) = (3,1 - y)

A:

Q: verify that (A + B) + C = A + (B + C)

A: Now,

Q: 1. Differentiate. Do not simplify. I b) g(x) = (7x3 – 3x² + x)(1+ 4x²) a) y = Vx4 -5x+1 d) g(x) =…

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

Q: Cakulate (3i+2j+k) • (i + zj - k

A:

Q: Find dy2 of z = 2x – 5xy² + x² y° %3D -

A:

Q: If ƒ (x, y) = x³y5 + 2xy, then what is the second coordinate of Vf? (Remember to use * for…

A:

Q: Exc. Eind. Lim (x-1) y3

A: Solution:

Q: -3-X, -3y, -3z]

A: We have to find div(V) from the given

Q: Find xy² Una -dA, R= [0,4] × [-2, 2] x² + 1

A:

Q: i want Z( zero) and Za

A: The known values are, x = 224, n = 237 The sample proportion is,

Q: Evaluate G r. d.x. (x2+1)(x+1) 0.

A: The following integrals are useful, while evaluating the integral that is provided. ∫dxx =ln x +C…

Q: 3x3-5x2+5 Different iate with respect to X. x2+1 (x²+1)2 Different iate with respect to x. x2-1

A:

Q: E Show that x'+ 3x+ 2 has 4 zerosin Ze

A: