Let A be a 2 2 matrix with linearly independent column vectors a1 and a2. If a1 and a2 are used to form a parallelogram P with altitude h (see the accompanying figure), show that (a) h2_a2_2 = _a1_2_a2_2 (aT 1 a2)2 (b) Area of P = |det(A)| h a1 a1 a2 a2 1

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