Determine unknown matrix from conditions

A question is this type if and only if it asks to find unknown matrix elements given information about how the transformation maps specific points or shapes.

1 questions · Moderate -0.3

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OCR Further Pure Core 2 2021 June Q2
5 marks Moderate -0.3
2 A 2-D transformation \(T\) is a shear which leaves the \(y\)-axis invariant and which transforms the object point \(( 2,1 )\) to the image point \(( 2,9 )\). \(A\) is the matrix which represents the transformation \(T\).
  1. Find A .
  2. By considering the determinant of A , explain why the area of a shape is invariant under T .