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 answer. %3D %3D

Q: Construct a linear map L(z)=az+b that will send the imaginary y-axis to the line v=-u.

A: we have to constract a linear map that maps the y-axis to the line v=-u Basically we have to…

Q: 8. X(2, 4) translated (x + 3, y– 3).

A:

Q: Find (2x + 5y)dA where Ris the parallelogram with vertices (0,0), (-5,4), (-2,-1), and (-7,3). Use…

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Q: If the midpoint of E (a-2,2a+3) U (1-3b,2b+1) and M is (6,3) find the value of a and b

A: I am going to solve the problem by using some simple geometry to get the required result of the…

Q: Make r the subject Y=x-r/x+r

A: Y = (x-r)/(x+r)

Q: What are the points of inter section of y = 8 and f(x)

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Q: O Find an equation for the plane through the point P = (3, −2, 4) that is perpendicular to the line…

A: Given problem:- Find an equation for the plane through the point P = (3, -2, 4) that is…

Q: t G(u, v) = (6u + v, 32u + 9v) be a map from the uv-plane to the xy-plane. Find the image of the…

A: We have to find the equation of line in slope intercept form.

Q: This table gives a few (, y) pairs of a line in the coordinate plane. -38 40 -23 30 -8 20 What is…

A: To find the x-intercept first we have to find the equation of line that passes through these point…

Q: The graphs of the functions y = ax² + bx + c on the plane xy are shown below, determine the…

A: The graph of a function is given as follows: y=ax2+bx+c   ........1 (a) The equation of a parabola…

Q: -6- and v3 3 7. Let vi , V2 = 5 9 2 -2 6. (a) show that {v1, V2, V3} is linearly dependent. (b) Find…

A:

Q: Find k so that the points P(0, 1, 1), Q(-1, 1, 3), and R(-3, 1, k) are on the same line (collinear).

A:

Q: Find x such that the points A(x, 5), B(2, 3), and C(4, - 5) are collinear.

A: Given. A(x,5), B(2,3) and C(4,-5) are collinear.

Q: Write v as a linear combination of u and w, if possible, where u = (2, 1) and w = (2, -2). (Enter…

A: u=2, 1 and  w=2, -2To express v=4, -1 as a linear combination of u and w

Q: calculate S S, y³ dA where Ris the vertex of the triangle (0, 2), ( 1,1) and (3, 2)|

A: In this question we have to calculate the following integral.

Q: Let G(u, v) = (5u + v, 30u + 13v) be a map from the uv-plane to the xy-plane. Find the image of the…

A:

Q: Construct a linear map L(z) = az + 6 that will send the imaginary y-axis to the line v = - u

A:

Q: Give an equation for the sphere with diameter PQ, where P = (1, 1,-5) and Q = (1,7,1). (Express…

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Q: I know the answer the question a. Kindly give me a nuanced response to the rest. I want to…

A: References Liu, D., Xue, S., Zhao, B., Luo, B., & Wei, Q. (2020). Adaptive dynamic programming…