MATLAB: How to find a standard matrix for a transformation

linear transformationmatrixmrdividestandard matrixtransformation

How could you find a standard matrix for a transformation T : R2 → R3 (a linear transformation) for which T([v1,v2]) = [v1,v2,v3] and T([v3,v4-10) = [v5,v6-10,v7] for a given v1,…,v7? I have been thinking about using a function but do not think this is the most efficient way to solve this question. Could anyone help me out here? Thanks in advance. Walter

Best Answer

Assuming the transformation is homogeneous - that is, it leaves the origin fixed - what you have here is six linear equations with six unknown coefficients. Just use standard matlab methods for solving them.
If the transformation is not necessarily homogeneous, then you don’t have enough information for a solution. You would need three instead of the two equalities above.
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