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Tis the reflection through the origin in RP: 7x, y) = (-X, Y), (3,2). (a) Find...
Consider the following. Tis the reflection through the origin in R2: T(x, y) = (-x, -y), v = (2,5). (a) Find the standard matrix A for the linear transformation T. A= 1 (b) Use A to find the image of the vector v. T(v) = (c) Sketch the graph of v and its image. у 6 у 6 V 5: 5 41 4 3 3 T(v) 2 2 11 1 X 1 -6 -5 -4 -3 -2 -1 -A 2...
Consider the following. T is the reflection through the origin in R2: T(x, y) = (-x, -y), v = (2,5). (a) Find the standard matrix A for the linear transformation T. A= (b) Use A to find the image of the vector v. T(V) =
Finding the Standard Matrix and the Image In Exercises 11–22, (a) find the standard matrix A for the linear transformation T, (b) use A to find the image of the vector v, and (c) sketch the graph of v and its image. T is the counterclockwise rotation of 120° in R2, v = (2, 2).
Find the standard matrix for the linear transformation T. T(x, y) = (3x + 2y, 3x – 2y) Submit Answer [-70.71 Points] DETAILS LARLINALG8 6.3.007. Use the standard matrix for the linear transformation T to find the image of the vector v. T(x, y, z) = (8x + y,7y - z), v = (0, 1, -1) T(v)
4. Let S be a plane in R3 passing through the origin, so that S is a two- dimensional subspace of R3. Say that a linear transformation T: R3 R3 is a reflection about Sif T(U) = v for any vector v in S and T(n) = -n whenever n is perpendicular to S. Let T be the linear transformation given by T(x) = Ar, 1 1 А -2 2 2 21 -2 2 3 T is a reflection about...
Consider the following T is the reflection in the y-axis in R2: T(x, y) (-x, y), v (2, -5) (a) Find the standard matrix A for the linear transformation T (b) Use A to find the image of the vector v (e) Sketch the graph of v and its image T (v) 5-4-3-21 T (v) T(v) 6 -5-4-3-2 6-5-4-3-2-1 239-lab 3 (2)pages F1 Assignment Submission For this assignment, you submit answers by question parts. The number of submissions remaining for...
2. Consider a reflection in the y-axis, dilation factor of In(2), rotation through, and a contraction factor of V7. A. Determine the matrix that defines this transformation. B. Determine the image of under this transformation. 2. Consider a reflection in the y-axis, dilation factor of In(2), rotation through, and a contraction factor of V7. A. Determine the matrix that defines this transformation. B. Determine the image of under this transformation.
Let L in R 3 be the line through the origin spanned by the vector v = 1 1 3 . Find the linear equations that define L, i.e., find a system of linear equations whose solutions are the points in L. (7) Give an example of a linear transformation from T : R 2 → R 3 with the following two properties: (a) T is not one-to-one, and (b) range(T) = ...
Question 1: (4+4 =8 Marks) [a] Show that the transformation 7(x, y) = (7x - 3y: 5x - 2y) of R4 R4 is a linear and give the matrix representation "A" of T with respect to the standard basis B={(1,0),0,1)). Furthermore, prove that T is invertible and find the preimage of the vector (1,-4). [b] Consider the transformation T: P3 → Pz defined by Tax3 + bx? +cx+d) = (a +2d)x? +(6+20)x² +(a+c+d)x. Determine Ker(T) and Range(T); and find a...
Let T : R2 → R2 be the linear transformation given by T(v) = Av that consists of a counterclockwise rotation about the origin through an angle of 30 2, Find the matrix that produces a counterclockwise rotation about the origin through an angle of 30°. Be sure to give the EXACT value of each entry in A. a. b. Plot the parallelogram whose vertices are given by the points A(0, 0), B(4, 0), C(5, 3), and D 1, 3)...