4) Find the standard matrix for RRR given by reflection through the plane y mz (mER). Hint: if we...
urgent please thank you very much (4) Find the matrix of reflection through the plane 2x-y-2z = 0 in R3. (7 points)
(4) (a) Determine the standard matrix A for the rotation r of R 3 around the z-axis through the angle π/3 counterclockwise. Hint: Use the matrix for the rotation around the origin in R 2 for the xy-plane. (b) Consider the rotation s of R 3 around the line spanned by h 1 2 3 i through the angle π/3 counterclockwise. Find a basis of R 3 for which the matrix [s]B,B is equal to A from (a). (c) Give...
Linear Algebra Problem 4: Given the normal vector n - 2 determine the matrix of the projection linear map through the plane (passing through the origin) which has n as a normal vector. Problem 5: Given the normal vector n = linear map through the plane (passing through the origin) which has n as a normal vector. V14' V14 V14 (#าพื้าพื้) determine the matrix of the reflection V14' V14 v14 Problem 4: Given the normal vector n - 2 determine...
Tis the reflection through the origin in RP: 7x, y) = (-X, Y), (3,2). (a) Find the standard matrix A for the linear transformation T. A- It (b) Use A to find the image of the vector v T(V) (c) Sketch the graph of vand its image. 3 T(v) 2 2 1 -3 2 - - 2 -1 2 1 3 -1 -1 -2 T(v) -31 -3 O T (v) 3 2 2 11 1
For each of the following, find the standard matrix of the given transformation from R2 to R2. (a) Clockwise rotation through 30° about the origin. a ab sin(a) 22 ar (b) Projection onto the line y = -42. a ab sin(a) !!! 22 8 (c) Reflection in the line y = 1 a ab sin(a) 22 ? Әr
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) =
For each of the following, find the standard matrix of the given transformation from R2 to R2 (a) Counterclockwise rotation through 120 about the origin. sin (a) f дх Ω (b) Projection onto the line y 5 x. sin (a) Ω да (c) Reflection in the line y= x- sin (a) Ω f
Problem: Given a rotation R of R3 about an arbitrary axis through a given angle find the matrix which represents R with respect to standard coordinates. Here are the details: The axis of rotation is the line L, spanned and oriented by the vector v (1,一1,-1) . Now rotate R3 about L through the angle t = 4 π according to the Right 3 Hand Rule Solution strategy: If we choose a right handed ordered ONB B- (a, b,r) for...
(Note: Each problem is worth 10 points). 1. Find the standard matrix for the linear transformation T: that first reflects points through the horizontal L-axis and then reflects points - through the vertical y-axis. 2. Show that the linear transformation T: R - R whose standard [ 2011 matrix is A= is onto but not one-to-one. - R$ whose standard 3. Show that the linear transformation T: R 0 1 matrix is A = 1 1 lov Lool is one-to-one...