5. Let T: R2 → R² be a linear transformation such that Nullspace (T) = {0}. Show that T takes: a) parallel lines to parallel lines. b) triangles to triangles. c) circles to ellipses.

Q: 5. Write a rule for the translation of a point of the plane figure above. A. (x,y)→ (x-2,y+3) B.…

A: Translation of a point of the plane means moving all the points of that plane to a new coordinate.

Q: Determine the geometric location of the points in R3 that equidistant from the plane y = 3 and the…

A: This is question of 3d geometry and locus.

Q: 60. Show that the distance between two points P1(x1, y1) and P2(x2, y2) is invariant under rotation.…

A: For the points P1 and P2 , the distance between the points is given d(P1,P2)=(x2-x1)2+y2-y12 . For a…

Q: Let G be the solid bounded by the parabolic cylinder x = y² - 2, and the planes z = 2x + 4 and z =…

A: Given : G be the solid bounded by the parabolic cylinder x=y2-2 and the planes z=2x+4 , z=4. To Find…

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: Let R be the parallelogram enclosed by the lines x + 3y = 0, x + 3y = 2, x + y = 1 and x + y = 4.…

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Q: Find the bilinear transformation which maps the points z = 0, -I, i onto w = i, 0, 0. Also find the…

A:

Q: it) is the point (-1,-2,3) visible from the point (1.2, 0) if there is an opaque ball of radius 1…

A: With the help of two points  then we find x,y and z values .. Then we put x,y and z values in…

Q: What kind of transformation results in applying the rule (x, y) → (x – 5, y) in the coordinate…

A:

Q: What are the projections of the point (−2, 3, 4) on the xy-, xz-, and yz-planes? Draw a picture and…

A: Given, the point (-2, 3, 4), we have to find the projections of this point on the xy-, yz-, and…

Q: △ABC△ABC has vertices A(0,4), B(6,-1), and C(3,7). What are the coordinates of C' when the triangle…

A:

Q: let l={(x,y) 7x+4y=1} be a line in Cartesian model for Euclidean geometry. find a coordinate…

A: Given: I=x, y 7x+4y=1 represents a line in Cartesian model.   To find: A coordinate function using…

Q: Prove that three points P(5,-4), Q(-3,8) and R(1,2) on the rectangular coordinate plane are…

A:

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: Complete the description of the transformation rule: (x, y) → ( x + 7, y - 15) Translate and

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Q: A rectangle ha verices at P (6, 6), Q (6, -6), R (-6, -6) and S (-6, 6). The origin is the center of…

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Q: must use linear algebra to find the parametric equations of a line of intersection in R3 for x1 + x2…

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Q: If (x1, yı) and (x2, y2) are distinct points in the plane, show that y 1 1 =0 X1 x2 y2 is the…

A: If (x1, y1) and (x2, y2) are distinct points in the plane, to show that  xy1x1y11x2y21 =0 is the…

Q: The triangle has vertices A(-2,3), B(0,0), and C(-1,-1). Plot the coordinates of the supermen logo…

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Q: Make a general statement regarding invariant points after a reflection in the x-axis and then in the…

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Q: Parametrize the directed line parabolic segment y = x2 that joins 2 + 4i to −1 + i.

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Q: Let r be the number of regions in a plane diagram of a 3-regular connected planar graph. Let v and…

A: Given : 3-regular connected planar graph