A: For each of the following maps T: V→ W, find the spaces V and W and say if they are linear or not (you must justify) 2. T(x, y) = (1, y)

Q: Show all the steps , thank you.

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Q: Choose a set S of three points such that aff S is the plane in R3 whose equation is x3 = 5. Justify…

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Q: Determine the intersection if any between the line L₁: [x, y, z] = [3, 2, − 5] + r[0, 1, 4] and the…

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Q: ✓1.22 Represent each linear map with respect to each pair of bases. (a) d/dx: Pn → Pn with respect…

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Q: Let r¡(t) = (-4,0, –5) + t(0, 1, –3) and r2(s) = (2, –2, 10) + s(2,0, 3). Find the point of…

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Q: Let A = (1, 0), B = (0, 1), C = (1, 1), and D = (r, 1). There are 24 orderings of the four points A,…

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Q: Let T V W be a linear map. : Show that Range T = Span{Tv₁,..., Suppose V Tvn}. = Span{V₁,..., Vn}.

A: Given : T : V→W be a linear map and  V = Spanv1, v2, ... , vn. To show : RangeT = SpanTv1, Tv2, ...…

Q: What is the image of a horizontal line y = k € R under the mapping W = 2²?

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Q: 2) Draw contour maps for functions f(x, y) = x² - 4y², and g(x, y) = x² + 4y². What shape. are these…

A: The contour of function f(x,y) represents parabolas.

Q: 1 -2 4 17. Let a 4 a2 -3 and b : For what 7 value(s) of h is b in the plane spanned by aj and a2?

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Q: Translate the image by the directed line segment from (0,0) to (4,1).

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Q: Let R denote the rectangle with corners (−1, −2), (4, −2), (4,1), and (-1,1), and let P denote the…

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Q: Find an equation for the set of points P(x, y) in a plane the sum of whose distances from two fixed…

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Q: Consider the points P = (1,2,0), Q = (0,1,2), and R=(2,0,1). Let A be an arbitrary point in…

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Q: 5. Evaluate - xy+3z)ds where C is the line starting at (1,1,1) and ending at (-1,-2,-3).

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Q: Let l1 : (x, y, z) = (131, 89, −83) + r (42, 28, −28) where r ∈ R and l2 : (x, y, z) = (29, 21,…

A: LetandShow that the lines  and  are identical.

Q: Sketch a contour map and graph of . a. g(x, y) = 9x² + 4y² b. z = y/x

A: The given function is: g(x, y) = 9x2 + 4y2 The contour map of the above function is:

Q: Describe and draw at least 3 level surfaces for the function f(r, y, z) = x²+ y? - z?

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Q: 3. Provide a small table and contour maps for the following functions. You need not attempt a three…

A: As per the question we have to provide a small table and contour maps for the following functions :…

Q: б. (a) Sketch the level curves z = k for k = 0, 1, 2 if z = x2 – y?.

A: The level curves of a function f of two variables are the curves with equations f(x, y) = c, where c…

Q: a) Mark the points on the contours where Iz = 0. b 2.

A: A contour line or level curve is the intersection of a surface with a horizontal plane. For example…

Q: Evaluate F(x,y,z) = (x3 +y³)i + (y³ + z³)j + (z³ + x³)k, and and S is the sphere with center the…

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