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Unformatted text preview: 0.00000 0.00000 1.00000 2.00000 3.00000 1.00000 which tells us that the inverse is A1 = 1 . 52 . 5 11 . 753 . 25 123 1 Example 4. Find 1 23 12 1 523 1 if it exists, and if it doesnt explain why. 1 Do the same thing, but this time the RREF is ans = 1.00000 0.00000 1.00000 0.00000 0.25000 0.25000 0.00000 1.00000 1.00000 0.00000 0.62500 0.12500 0.00000 0.00000 0.00000 1.00000 1.50000 0.50000 Since the left side of the partition is NOT an identity matrix (note the row of zeros!) we conclude that A is not invertible. 3. A fact about singular matrices Theorem 5. A matrix is singular if and only if the homogeneous system Ax = 0 has a nontrivial solution. This observation is important later (e.g. when were trying to gure out how to nd eigenvalues and eigenvectors). 2...
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 Spring '08
 Bens
 Linear Algebra, Algebra, Matrices

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