MTH 341 Midterm: MATH 341 Oregon State MidtermSampSol
31 Jan 2019
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If you have any questions about what you are supposed to do ask! The real midterm will take place in class, 1-1:50pm on friday 2 november: let a be the 3 3 matrix. 4 2 3 and let i denote the 3 3 identity matrix. Now consider the following three linear systems, given in matrix form as (a + i)~x = Among these three systems, identify the one that has a unique solution, the one that has in nitely many solutions, and the one that has no solution. Since a is lower triangular, the same is true for each of a+i, a 2i, and a i. Thus their determinants are easy to calculate by taking the product of the diagonal entries. In particular, det(a + i) 6= 0, so any linear system with coe cient matrix a + i has a unique solution. On the other hand, the determinant of a i is zero so the invertibility.
