Find the linear or affine transformations that satisty the desired properties and write it in the form T(x)=Ax + b: The transformation T : R2 → R2 sending the origin to itself and a triangle of vertices (0, 0), (1, 0), (0, 1) to a triangle of verices (0, 0), (22, 22), (−22, 2).

Question

Find the linear or affine transformations that satisty the desired properties and write it in the form T(x)=Ax + b:  The transformation T : R2 → R2 sending the origin to itself and a triangle of vertices  (0, 0), (1, 0), (0, 1) to a triangle of verices (0, 0),  (22, 22), (−22, 2).

Khribechy · Accepted Answer

We have the tranformation as, T→(t1 : t2)=(−1)det(0x→y→z→t1a1b1c1t2a2b2c21111)det(a1b1c1a2b2c2111) Graphical representation:  The red triangle is transformed into blue triangle under the transformation T. Here, T→(t1 : t2)=(−1)det(0x→y→z→t1a1b1c1t2a2b2c21111)det(a1b1c1a2b2c2111) =det(0x→y→z→t1010t20011111)det(010001111) = −x→t1 − y→t1 + x→t2 − x→ − z→t21 =(y→ − x→)t1 + (z→ − x→)t2 + x→ Now, plugging in the transformed entries. =((2222) − (00))t1 + ((2222) − (00))t2 + (00) =(2222)t1 + (−2222)t2

Find the linear or affine transformations that satisty the desired properties and write it in the form T(x) = Ax + b: The transformation T : mathbb{R}

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