MATH 1025 Lecture Notes - Augmented Matrix, Gaussian Elimination, Coefficient Matrix
11 Apr 2023
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Class 4: solutions to systems of equations, homogeneous systems, rank: (warm up. ) Consider the system of equations with augmented matrix shown on the left below. We can use the row reduction algorithm (gaussian elimination) to obtain the rref of this matrix, shown on the right. Options: (a) one solution (b) no solutions (c) in nitely many solutions. We can make some general conclusions based on our calculations in the previous question and from last time: no solutions. The system of equations will have no solutions if: one solution. The system of equations will have exactly one solution if, when the corresponding augmented matrix is reduced to rref, on the left side of the vertical line: in nitely many solutions. The system of equations will have in nitely many solutions if, when the corresponding augmented matrix is reduced to rref, on the left side of the vertical line:
