(5.9) Example: Prove f: R² x R? →, define by f((x1,y1), (x2,Y2)) = x1X2 – YıYz is symmetric bilinear map. sol. 1- f is bilinear map(H.W). 2- VA = (x1, y1), B = (x2, Yz) E R² , f(A, B) = f((x1,Yı), (X2, Yz)) = X1X2 - YıYz=X2X1 – Y2Yı = f((x2, y2), (x1, Yı)) = f(B,A) %3D

Q: III) Suppose that the linear map T: R-R' satisfies 00 0-0-0-0-0-0 2 2. What are det T and trace T?

A: Given :-  Suppose that the linear map T : ℝ4 → ℝ4 satisfies T 1000 = 2622 ,  T 0100 = 1311 ,  T 0010…

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Q: (a) Show conclusively that the map f : R² → R defined by f(x, y) = x cos(y) is not linear.

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Q: 7. Find the Jacobian of the transformation T(x, y) = (w sin(v²),w cos(v²)). X=w Sin (v?) w = sin…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question (Q7) for you.…

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A: First find matrix then find rank

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A: As per our norms we have to write one question at a time kindly repost remaining questions.

Q: Which of the following maps is not linear? А. T:R²→R² defined by T(x,y) = (x²2,x+y)· В. f:R3→R2…

A:

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Q: 3. Use Green's Theorem to evaluate G³ï+xj)•dr around the perimeter of the rectangle 0<x<2,0<y<3.…

A: Given ∫C(y2i+xj).dr We know that dr = dxi+dyj Thus ∫C(y2i+xj).dr = ∫C(y2i+xj).(dxi+dyj)  =…

Q: 2. Consider the function f(z) = ( -3) on (0, 1]. (a) Prove that / for r, ye 0, 1], (b) Prove that /…

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A:

Q: 1. Let T: R3 -> IR3 the linear map defined by T (x, y, z) = (y + 2, x + z, x + y). Tis she…

A: We will find out the required inverse linear map if given map is invertible.

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A: According to bartleby honor code and guidelines we have to do only first question

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Q: . Show that the mapping a: E² → E², (x, y) – (3y, x + 2) is a transformation and a collineation by…

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Q: Given the map f:R3 R4 defined by f(x,y,z) = (0,0,0,0) then rank of f is:

A:

Q: Given the map f: R3→R4 defined by f(x,y,z) = (0,0,x,0) then nullity of f is: А. 0- В. 2. С. 3- O D.…

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Q: Show that dim(W1) + dim(W2) – dim(W1n W2) = dim(W1 + W2), where W1 + W½ just denotes the span of W1…

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Q: Please solve

A: Consider the given function.

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A: Here we have to find out line integral of function f(X,Y,Z).

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A:

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A: Given,            F(x, y, z)=x2y+ez, yz-x

Q: Consider the following linear maps T : R² → Rª and S : Rª – M(2,R) defined as follows: 2x + 3y T(…

A: The solution is below.

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Q: consider the map given by F(x)=1-x² discuss the charactristics of the orbits starting at x=0

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Q: Exercise 4.1. Let F : R² → R² be the map defined by F (;) = () for any () E R². Describe the image…

A: Let ab∈R2 If ab satisfies x2+y2=1 then, 2a3b satisfies the equation x22+y32=1.

Q: Let ƒ (x, y) = x² - y² . Find all all points (x, y) such that Vf(x,y) =±(1, 1).

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.