MIT
18 06 -
Lecture 3
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Lecture 3 Review ax b square A E E Ax E E b Ux c Back Substitution What can go wrong perfect case n pivots no exchange good case n pivots with exchange A LU PA LU singular case n pivots Inverse of A A A I and AA I Testings to nd an inverse Elimination succeeds n pivots If Ax 0 has a solution x 0 then A is not invertible If Ax 0 and if A is invertible A Ax A 0 because x 0 Finding the inverse of a 2x2 matrix If the determinant is zero the matrix is not invertible the matrix is singular det pivot 1 pivot n Gauss Jordan trying to nd the inverse of A We know that AA I We can break this down and write Finding the inverse of a 2x2 matrix Permutation PA LU Exchanges the rows
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