sample test 1

sample test 1 - MATH1850/2050 S09 Name: Page 1 of 6 (1) (6...

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MATH1850/2050 S09 Name: Page 1 of 6 (1) (6 marks) Solve the linear systems associated with the following matrices: ( i ) 1 3 0 - 1 4 0 0 1 2 3 0 0 0 0 0 ( ii ) 1 3 - 2 5 0 1 2 - 2 0 0 1 - 1 (2) (5 marks) Find conditions on b 1 ,b 2 ,b 3 such that the following system is consistent: x 1 + 2 x 2 - x 3 = b 1 2 x 1 + 5 x 2 - 3 x 3 = b 2 3 x 1 + 7 x 2 - 4 x 3 = b 3
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MATH1850/2050 S09 Name: Page 2 of 6 (3) (5 marks) Find the inverse of the following matrix (make sure you label all your row operations and state what A - 1 is explicitly): A = 1 0 1 0 - 2 0 - 1 0 0 2 0 0 2 0 2 1
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MATH1850/2050 S09 Name: Page 3 of 6 (4) (5 marks) For which values of k does A fail to be invertible? A = 1 - 2 - 5 - 1 k 6 2 - 4 k + 2 (5) (4 marks) Solve for the matrix B in the following matrix identity ( show all steps, and mind the order of operations ): ( 1 2 B T - I 2 ) - 1 = ± 5 - 2 2 - 1 ²
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MATH1850/2050 S09 Name: Page 4 of 6 (6) (3 marks) Find the second row of the matrix product AB where A
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sample test 1 - MATH1850/2050 S09 Name: Page 1 of 6 (1) (6...

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