MT2 Review - Solutions

# MT2 Review - Solutions - Math 54 Midterm 2 Review Mike...

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Math 54 Midterm 2 Review Mike Hartglass November 7, 2010 1.) True/False: a. ) If A is row equivalent to 1 0 0 4 then the eigenvalues of A are 1 and 4. False b. ) If A is diagonalizable then the columns of A are linearly independent. False c. ) The matrix 1 2 3 2 3 4 3 4 5 is diagonalizable. True d. ) The matrix 1 1 0 0 1 0 0 0 2 is diagonalizable. False e. ) The matrices 1 3 π 47 0 4 8 5 0 0 e π 4 π 0 0 0 2 and 1 - 4 e 2 20 0 4 42! 5 0 0 e π - 33 0 0 0 2 are similar. True f. ) If A and B are invertible n × n matrices, then AB is similar to BA . True g. ) If A and B are arbitrary n × n matrices then AB is similar to BA . 1

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False h. ) If A is an n × p matrix then the equation A T Ax = A T b always has a solution for x R p and b R n . True i. ) An orthogonal matrix is one which has orthogonal columns. False. This is not the definition of an orthogonal matrix. Need the columns to have norm 1.
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