11. APQR with vertices P(4,2), Q(3,-3) and R(5,-2) is a transformation of AJKL with vertices J(-2,0), K(-3,-5), and L(-1,-4). Graph the original figure and itsimage. Identify the transformation.
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- Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).Why does every linear transformation T from R 2 to R 2 take squares to parallelograms? Rectangles also go to parallelograms (squashed if T is not invertible).Sketch the image of the rectangle with vertices at (0, 0), (1, 0), (1, 2), and (0, 2) under the specified transformation.T is the expansion represented by T(x, y) = (2x, y).
- Decide whether the transformation T (x, y) = (4x − 3y, 3x + 4y) is a similarity transformation. If so, what is the multiplier m?Is there a linear transformation T : R3 --> R2 such that T(1, 0. 3) = (1, 1)and T ( -2, 0, -6} = (2, 1)?***PLEASE HELP WITH THE FOLLOWING AND PLEASE PROVIDE HANDWRITTEN WORK ON PAPER*** (6) Let T R3 --> R3 be a linear transformation such that T(1,1,1) = (2,0,-1), T(0,-1,2) = (-3,2,-1) and T (1,0,1) = (1,1,0) find T (2, -1,1)
- Consider the transformation T: x=12/37u − 35/37v, y=35/37u + 12/37v The transformation is linear, which implies that it transforms lines into lines. Thus, it transforms the square S:−37≤u≤37,−37≤v≤37 into a square T(S) with vertices: T(37, 37) = ( _ , _ ) T(-37, 37) = ( _ , _ ) T(37, -37) = ( _ , _ ) T(-37, -37) = ( _ , _ )What are the coordinates of U′ for the transformation ( T < − 3 , 1 > ∘ D 4 ) ( Δ T U V )of T(−7, −6), U(−8, 3), and V(2, 1)?Suppose a linear transformation: T:R2-->R2 is formed by taking a rotation counterclockwise of 180 degrees, followed by a reflection across the x2-axis. Describe the points that will be moved back to their original position by this transformation.
- Compute the Wronskian for 2t^2y''+3ty'-y=0The ABC Toy Company is creating two similar pieces for a board game, as shown below. How could the toy maker confirm that the pieces are similar using the definition of similarity in terms of similarity transformations? triangles GHI and JKL Verify ∠G ≅ ∠J and ∠I ≅ ∠L by reflection. Verify segment GH ≅ segment JK and segment GI ≅ segment JL by reflection. Verify ∠G ≅ ∠J and ∠I ≅ ∠L by translation. Verify segment GH ≅ segment JK and segment GI ≅ segment JL by translation.Apply the transformation T (x, y) = (0.8x − 0.6y, 0.6x + 0.8y) to the scalene triangle whose vertices are (0, 0), (5, 0), and (0, 10). What kind of isometry does T seem to be? Be as specific as you can, and provide numerical evidence for your conclusion.
