MATH 551 Midterm: MATH 551 KSU Test1SampleWithSolutions s07
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15 Feb 2019
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In each of the following cases we are dealing with a system ax = b. Each case has a di erent coe cient matrix a and a di erent right hand side vector b. Also, in each case we are told what rref([a b]) is. Now, in each case determine the following: size of the matrix a (number of rows and number of columns, an expression for the solution(s) to the system (if the system has no solutions, point that out). In the case of having in nitely many solutions, also indicate the number of free variables. Here a is 3 4 and there are in nitely many solutions with 1 free variable. x1 = 7, x2 = x3, x3 is free, and x4 = 4. A is 5 3 and there is a unique solution x1 = 0, x2 = 0, and x3 = 0. A is 5 4 and the last row makes the system inconsistent.
