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 Linear transform
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Manu
Average Member

Australia
9 Posts

Posted - 03/28/2012 :  10:32:10  Show Profile  Reply with Quote
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-plane

T2 projects orthogonally onto the xz-plane

T3 rotates clockwise through an angle of 3π/4 radians about the y axis

1. 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.
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Ultraglide
Advanced Member

Canada
299 Posts

Posted - 03/31/2012 :  12:00:25  Show Profile  Reply with Quote
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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