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(d) (3 pts) T: R2 + R2 first reflects points through the 11-axis and then reflects...
Let T:R2 → R2 be the linear transformation that first reflects points through the x-axis and then then reflects points through the line y = -x. Find the standard matrix A for T.
Let T:R? → Rº be the linear transformation that first rotates points clockwise through 30° (7/6 radians) and then reflects points through the line y = 2. Find the standard matrix A for T. A=
Give a linear transformation from R2 to R2 that first reflects a point over the y-axisrotation.and then rotates it π2 radians counterclockwise about the origin in two ways:
Assume that is a linear transformation. Find the standard matrix of T. T: R2R2 first rotates points through - radians and then reflects points through the horizontal Xy-axis. (Type an integer or simplified fraction for each matrix element. Type exact answers, using radicals as needed.)
Assume that T is a linear transformation. Find the standard matrix of T. TR2-R2, first performs a horizontal shear that transforms e into ez + 18e, (leaving e, unchanged) and then reflects points through the line Xz = -X (Type an integer or simplified fraction for each matrix element.)
i need help with this question. it is from linear algebra Assume that T is a linear transformation. Find the standard matrix of T 5T radians and then reflects points through the horizontal x-axis T: R2R2 first rotates points through 3 A= (Type an integer or simplified fraction for each matrix element. Type exact answers, using radicals as needed.)
3. (6 points/2 each) Let T:R2 + R2. State why T is not linear. (a) T(C1, C2) = (1, 1). (b) T(1, 2) = ( 1,). (c) T(x1, x2) = (1 + x1, x2).
4. (22 points) Let To : R2 R2 be the linear transformation that rotates each point in IR2 about the origin through an angle of θ (with counterclockwise corresponding to a positive angle), and let T,p : R2 → R2 be defined similarly for the angle φ. (a) (8 points) Find the standard matrices for the linear transformations To and To. That is, let A be the matrix associated with Tip, and let B be the matrix associated with To....
(12) (after 3.3) (a) Find a linear transformation T. Rº Rº such that T(x) = Ax that reflects a vector (1), 12) about the Tz-axis. (b) Find a linear transformation SR2 R2 such that T(x) = Bx that rotates a vector (2, 2) counterclockwise by 135 degrees. (c) Find a linear transformation (with domain and codomain) that has the effect of first reflecting as in (a) and then rotating as in (b). Give the matrix of this transformation explicitly. How...
(a) Let T: R2 + R2 be counter clockwise rotation by 7/3, i.e. T(x) is the vector obtained by rotating x counter clockwise by 7/3 around 0. Without computing any matrices, what would you expect det (T) to be? (Does T make areas larger or smaller?) Now check your answer by using the fact that the matrix for counter clockwise rotation by is cos(0) - sin(0)] A A= sin(0) cos(0) (b) Same question as (a), only this time let T...