Began by explaining the gaussian elimination algorithm, and by noting that it fails when a pivot is zero.

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Then defined the determinant and adjoint of a 2&times;2 matrix. Gave a formula for the inverse of a 2&times;2 matrix in terms of its determinant and adjoint. Explained that the determinant of a 2&times;2 matrix is equal to the area of a certain parallelogram up to sign.