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Manu
Average Member

Australia
9 Posts

 Posted - 03/28/2012 :  10:32:10 Given below are three geometrically defined linear transformations from R3 to R3. You are asked to find the standard matrices of these linear transformations, and to find the images of some points or sets of points.T1 reflects through the yz-planeT2 projects orthogonally onto the xz-planeT3 rotates clockwise through an angle of 3π/4 radians about the y axis1. The standard matrix of T1 is (-1,0,0 0,1,0 0,0,1)2. The standard matrix of T2 is___________________3. The image under T1 of the line segment joining the points (2, -2, 4) and (-2, 3, 3) is line segment joining the points________________and________________4. The point (-4, 3, 3) is first mapped by T2 and then T3. The coordinates of the resulting point are______________________I don't know how to start for 2,3 and 4. Any help would be great.

Ultraglide

299 Posts

 Posted - 03/31/2012 :  12:00:25 For #3, to get the image of (2, -2, 4) under the transformation, multiply the 1x3 matrix (row by column) by the 3x3 matrix.
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