FinalSample - C A where A = 1 1 1 1 1-1 1-1 1-1(b Find the...

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APAM-Linear Algebra: Final exam sample 2009
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1. (a) For the following 3 x 3 matrix A , compute its determinant by using the cofactor formula and expanding along the third column. Show the values of the 3 cofactors you compute. A = 1 2 3 - 1 2 - 2 1 - 4 1 . (b) Consider the matrix B obtained from A by adding rows 1 and 3 to row 2. Should det( B ) equal det( A )? Why? 2. Give all values of x for which A has an eigenvalue equal to 2. A = 3 2 - 1 2 x 2 x - 2 3 . 3. (a) Use the Gram-Schmidt procedure to find an orthonormal basis of
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Unformatted text preview: C ( A ) where: A = 1 1 1 1 1-1 1-1 1-1 . (b) Find the projection matrix P for projecting onto C ( A ) . Recall that with the factorization A = QR , the projection matrix P = A ( A T A ) ?1 A T becomes QQ T . (c) Check your answer for P by computing Pa 1 where a 1 is the first column of A . 1...
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