Let D be a parallelogram with vertices (0,0), (2,1), (2,3), (4,4) Find a linear transformation x=x(u,v), y=y(u,v) and use to evaluate a. b. C. d. (x + y)dA 35 2 16 32 3 12

Q: 7. Is this a linearly independent subset of R³ ? {(1, 4, −6), (1, 5, 8), (2, 1, 1), (0, 1, 0)}…

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Q: Let B To which point do the linear maps associated with A and B map the points (1, – 9) and (4, 4)?…

A: we know  Tx=Ax Given,  A=1038B=-40-12

Q: 5. The triangle with vertices at (2, 3), (4,6) and (5, 10) is transformed by the matrix T where T=…

A: It is given that the vertices of the triangle are 2, 3, 4, 6 and 5, 10. First we have to sketch the…

Q: Let T: R³ – R³ be a linear transformation such that T(1, 0, 0) = (2, –1, 4), T(0, 1, 0) = (-2, 3,…

A: Given that:T:ℝ3→ℝ3T1, 0, 0=2, -1, 4T0, 1, 0=-2, 3, 1T0, 0, 1=2, 0, -2To find: T-4, 2, 1

Q: Question 8 Consider the square with vertices (0, 0), (1, 0), (1, 1) and (0, 1). The matrix T, = ( )…

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Q: Show that the line [x, y, z]= [5,-1,3]+[4,-5,2] lies on the planes 3x+2y-z = 10 and 7x+4y-4z=19.

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Q: Find (2x + 3y)dA where R is the parallelogram with vertices (0,0), (-1,-4), (-3,-2), R and (-4,-6).…

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Q: Evaluate ff(6x - 3y)dA region bounded by the parallelogram with vertices (2, 0), (5, 3), (6, 7) and…

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Q: Let ui = (3, –1,3, 3), u2 = (-2,3, 1, 3), and uz = (0, –1, -1, –1). Write v = (8, –9, 1, –1) as a…

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Q: Suppose T: R2 → R2 is a linear transformation. The figure shows where I maps vectors V₁ and V2 from…

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Q: d 3. Find the herrel of the linear transformati L: R³ R³ with matrix 2 5 1 390 1 4 -1

A: To find kernel, we have to find null space of corresponding matrix.

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

A: We  have  to  find a  linear  transformation T: ℝ3 →ℝ3   for  which…

Q: 6) translation: (x, y) → (x + 1, y) K M A) K(-4, 4), L(-2, 5), M(-3, 1) B) K(-5, 3), L(-3, 4), M(-4,…

A: The solution are next step

Q: 3. Find an equation for the plane in R³ containing the points P = (4, 1, 0) Q=(3, 2, 1) R = (5, 1,…

A: The given points are, P=(4,1,0)Q=(3,2,1)R=(5,1,1). Let an equation containing three points…

Q: roțațion 90° counterclockwise about the origin U(0, -2), V(-1, 2), w(1, 3), x(4, 0) A) U(0, 2), V(1,…

A:

Q: 5. Let B = {b₁,b2}, where b₁ = √(1,3), b2 = √(-3,1). (a) Specify the transition matrices Ps,B and…

A: The given vectors are b1=1101,3, b2=110-3,1. The given line is y=3x.

Q: 4. Find an equation of the plane that passes through the points P(1,3,2), Q(3,–1,6), and R(5,2,0).…

A: Given points P1,3,2, Q3,-1,6, R5,2,0

Q: 4. Find an equation for the plane in R³ spanned by the points (1,5, 1) and (1, 4, 2).

A: The two vectors are given as v1 = 151v2 = 142 Let xyz∈span{v1 , v2} Then xyz = mv1+nv2= m151+n142=…

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

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

Q: Show that the set S= {(20, 34), (40, 68)} is linearly independent or not?

A: Given set is S= {(20, 34), (40, 68)}

Q: Q1. Consider the 3D shape with the following vertices: 4-38-60-60-98-88-8 A=5,B=5,C = 5,D = 5,E =…

A: Step 1: Step 2: Step 3: Step 4:

Q: 3. a) Is there exists a linear map T: R2 R2 for which T(7,7)=(4,-5) and T(2,2)=(8,-2)? Justify your…

A: