Question: Let A be a 2 x 2 matrix with linearly independent column vectors a1 and a2. If a1 and a2 are used to form a

Let A be a 2 x 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 figure), show that
(a) h2||a2||2 = l|a1||2||a2||2 - (aT1a2)2
(b) Area of P = |det(A)|

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