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201mt1sln

# 201mt1sln - B U Department of Mathematics Math 201 Matrix...

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B U Department of Mathematics Math 201 Matrix Theory Date: March 25, 2008 Full Name ( In ink ) : Time: 17:00-18:20 Student ID : Math 201 Number : Spring 2008 First Midterm IMPORTANT 1. Write your name, surname on top of each page. 2. The exam consists of 4 questions some of which have more than one part. 3. Read the questions carefully and write your answers neatly. 4. Show all your work. Correct answers without sufficient explanation might not get full credit. 5. Calculators are not allowed. Q1 Q2 Q3 Q4 total 10 pts 16 pts 14 pts 20 pts 60 pts 1. a) [8] Find the inverse, if exists, of the following matrix using the Gauss-Jordan method: A = 1 3 0 2 5 1 - 3 - 9 - 1 Solution: 1 3 0 : 1 0 0 2 5 1 : 0 1 0 - 3 - 9 - 1 : 0 0 1 - 2 r 1 + r 2 r 2 -------→ 3 r 1 + r 3 r 3 1 3 0 : 1 0 0 0 - 1 1 : - 2 1 0 0 0 - 1 : 3 0 1 r 3 + r 2 cr 2 -----→ - r 3 r 3 1 3 0 : 1 0 0 0 - 1 0 : 1 1 1 0 0 1 : - 3 0 - 1 3 r 2 + r 1 r 1 ------→ - r 2 r 2 1 o 0 : 4 3 3 0 1 0 : - 1 - 1 - 1 0 0 1 : - 3 0 - 1 A - 1 = 4 3 3 - 1 - 1 - 1 - 3 0 - 1 b) [2] Find the inverse, if exists, of the matrix B = 1 2 - 3 3 5 - 9 0 1 - 1 . Solution: Observe that B = A T .

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