Fall 2009 Midterm #1

Fall 2009 Midterm #1 - MATH1850/2050 S09 (1) (6 marks) 1 0...

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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 k such that the following system has (i) exactly one solution, (ii) no solution, (iii) -many solutions. 2 x 1 + 2 kx 2 = 4 3 x 1 + ( k 2 + 2) x 2 = k + 4
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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 0 1 0 0 2 0 2 1 1 1 - 2 0 0 - 1
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MATH1850/2050 S09 Name: Page 3 of 6 (4) (5 marks) Determine the value(s) of k for which A fails to be invertible A = 1 - 3 - 4 2 - 6 k - 3 - 2 k + 1 5 (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 - 3 I 2 ) - 1 = ± 3 - 4 2 - 2 ²
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MATH1850/2050 S09 Name: Page 4 of 6 (6) (3 marks) Find the second row, third column
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Fall 2009 Midterm #1 - MATH1850/2050 S09 (1) (6 marks) 1 0...

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