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Fall 2010 Midterm #1 Solutions

# Fall 2010 Midterm #1 Solutions - MATH1850 Midterm 1 October...

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MATH1850 Midterm 1 October, 2010 2 1. (3 marks each; total 6 marks) Solve the linear systems associated with the following augmented matrices. Hint: They are already either in reduced row-echelon or row-echelon form for you. a) 0 0 0 0 0 2 7 2 1 0 1 2 5 0 1 b) 7 1 0 0 3 5 1 0 2 4 1 1

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MATH1850 Midterm 1 October, 2010 3 2. (7 marks) Evaluate the determinant of the following matrix. You may use any method as long as it is correct. 2 1 2 0 0 0 3 5 1 1 2 1 5 4 0 1 A
MATH1850 Midterm 1 October, 2010 4 3. (5 marks) Given the system b x A with 5 3 4 1 A and 2 8 b , use Cramer’s Rule to find 2 x . You must use Cramer’s Rule…other methods will not receive marks. 4. (4 marks) Let A be a square matrix such that A I is invertible. Prove that 3 2 1 ) ( A A A I A I if 0 4 A (i.e. if 4 A is a matrix of zeroes).

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Fall 2010 Midterm #1 Solutions - MATH1850 Midterm 1 October...

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