Suppose that T: R³ → R³ is a linear map, and ... T -0-0 T2 = Then F O O O 0- = ... [] 00 сл 2 H 23 6 H 7 сл 4 7 2 and T 0 = N

Q: Show all the steps , thank you.

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Q: {(x, y) : x s 1, y < 2} О -4 -3 -2 -1 -4 -3 -2 -1 у 4 3 2 1 - 1 -2 -3 -4 y 4 3 2 1 -1 -2- -3 2 3 4 2…

A: We draw the graph of {( x, y ) : x ≤ 1, y &lt; 2}

Q: Suppose that L1 is the line through point (1, 2, 3) with direction vector [2 ,- 3 ,0]t. And suppose…

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Q: Which one of the following is an equation of the line through points P(1,-1, 2, 1) and Q(3, 1,…

A: We have to find an equation of the line passing through points P(1,-1,2,1) and Q((3,1,1,-1)

Q: C: 1. Is there a linear map from R2 to R³ such that T(1, 3) = (0, 0, 0) and T(-2,0) = (0, 0, 0) and…

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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: Determine the point of intersection of the lines. 4:[x, y, z]=[-3, 1, 4]+s[-1, 1, 4] (2:[x, y, z] =…

A: Let (a,b,c) denote the point of intersection So, For l1a=-3-s0b=1+s0c = 4+4s0For l2,a =…

Q: -3 Let S = 33 1 a. Find span(S). b. Is S linearly independent? C. Is -3 0 in in the span(S)?

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Q: Let C C R³ be the directed line segment from (1, 1, 1) to (3, 2,0). Evaluate

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Q: 1. The map T : Mat2,2(R) → Mat2,2(R) given by a +c d a b T c d а — d

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Q: Show that these two lines are coincident. L1: [x, y, z ] = [1, 5, − 2] + s [1, 7, − 3] L2: [x, y, z…

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Q: A bird takes exactly two minutes to fly linearly from P(3,8,4) to Q(7,4,-3). Assuming that the bird…

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Q: 4. Consider the the linear maps f: R² R² and g: R² R² given by f((x, y)) = (x-y,2+ y) and g((x, y))=…

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Q: Suppose that T: R³ R³ is a linear map, and ... T2 = ·-· ----· 2 and T Then B T 3 25 13 3 10 36 23 78…

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Q: 2. Evaluate [ F C F = (xz, 0, yz) and the path C is the line segment from point (-1,2,0) to (3,0,1)…

A: Given that, Now,

Q: .. A projective transformation M preserves the points (1,0,0), (0,1,0), and the origin of the…

A: according to question , a projective transformation M preserves the point 1,0,0 , 0,1,0 and 0,0,0…

Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

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Q: 2. Find the value of k so that the line [x, y, z] = [2, -2, 0] + t[3, 5, k] is parallel to the plane…

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Q: 157 Find the linear mapping f(z)=9| e 4 z+8i applied to the circumference | z-i |-7. 2

A: We know that eiθ=cosθ+isinθ ∴ei5π4=cos5π4+isin5π4             =cosπ+π4+isinπ+π4             =-12-i12…

Q: . Decide which of the following sets are linearly independent in R. Justify your answer in each…

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Q: Find a plane containing the lines x = 3+ 21 x =1- 21 y = 4– 31 and y = 7+41 where -o <t<00, z =1-31.…

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Q: Let F = Vf and f = 5x²y - 5z. Calculate F. dr for the path r₁ = (t, t,0), 0 ≤ t ≤ 1. (Give your…

A: We will use fundamental theorem of line integrals

Q: 1. Sketch the graph of the domain of the function f (x, y)= sq x / x−y​ 2. Compute the equation of…

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Q: For each of the following, determine (with argument) whether the given function T is linear. 1. The…

A: To identify which of the given function is linear transformation.

Q: CHCIE 2 8-8-8-8 t₁0+t₂ 1 2 0 5 Show that 3 is in the linear span of 0 10 5 3 = 10 - by finding t1,…

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Q: Need only handwritten solution only (not typed one).

A: The given set .To find the image of the set  under the transformation .

Q: 10. Show that these two lines are coincident. [x, y, z]= [1, 5, -2]+s[1, 7, -3] [x, y, z]=[-3, -23,…

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Q: Q.5. D.] find the Cartesian equation of the plane r(u, v) (u,v + 2,3u-2v), -1≤u≤2 and -2≤0≤3

A: To find the cartesian equation of the plane from a given parametric equation, we need to eliminate…

Q: (y – 2)² Draw a contour map of z = r² + using k = 0, 1,2, 3, 4, then sketch its graph in 9 R³.

A: The graph of a three dimensional surface is represented by the equation: z=f(x,y). The graph of a…

Q: 7. Consider the ordered bases S and T of R: ()} S = {81, 82, $3} and T = {t1, t2, t3} = We define a…

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Q: 3. Evaluate (2ry - )+(r +2:)7+(2y- 2r2)k) - dr, where C is a simple curve from (-3,-2,-1) to (1, 2,…

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