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6 Nov 2019
Let and be non-parallel vectors in R2. Recall that we can define the cross product of vectors in R2 by adding a 0 component: We also know that where theta is the angle between and Using these facts, prove that the area of the parallelogram P defined by and is given by Let A be any invertible 2 times 2 matrix. Prove that and also define a parallelogram. Call this new parallelogram P'. Prove that Area(P') = |det(A)|Area(P). Show transcribed image text
Let and be non-parallel vectors in R2. Recall that we can define the cross product of vectors in R2 by adding a 0 component: We also know that where theta is the angle between and Using these facts, prove that the area of the parallelogram P defined by and is given by Let A be any invertible 2 times 2 matrix. Prove that and also define a parallelogram. Call this new parallelogram P'. Prove that Area(P') = |det(A)|Area(P).
Show transcribed image text