Linear algebra practice.?

Linear algebra practice.?



Having trouble with this practice problem for my linear algebra class.

2. Affine Transformation in the Plane
(a) Determine the standard matrix, A, of the transformation that combines the
following into one transformation:
– a scaling factor of 2 in the x-direction
– a scaling factor of 1/2 in the y-direction
– a shear of factor 2 in the y-direction

I think my transformation matrix for this would be something like:
[ 2 0 ]
[ 0 (2).5 ]

(b) Now determine the affine transformation T(~x) = A~x+~v that uses the matrix
from part (a) and a vector that will translate the origin to the point (5, ?5).

This I dont really know where to start :- /





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