MAT280-Su20 - MidTermReview.docx - MAT 280 Mid-Term Review...

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MAT 280 Mid-Term Review 1. Determine all solutions to the system: x 1 + x 3 = 2 x 1 + x 2 + x 3 + 4 x 4 = 5 x 2 2 x 3 = 0 2 x 1 + x 2 4 x 3 4 x 4 =− 3 2. In a certain town people have cable TV, satellite TV, or antenna TV. In the next year, 70% of those with cable TV will keep cable TV and 20% will switch to satellite TV, 80% of those with satellite TV will keep satellite TV and 5% will switch to antenna TV, and 70% of those with antenna TV will keep antenna TV and 15% will switch to cable TV. Currently, 40% of homes have cable TV, 50% have satellite TV, and 10% have antenna TV. What will these percentages be in 6 years? 3. Calculate the following determinant: | 1 2 1 1 0 4 0 0 0 1 1 2 1 3 1 1 | 4. a. Construct the transition matrix from the basis B = { ( 0,1 ) ; ( 2,1

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