MTH 141 Lecture Notes - Lecture 26: Linear Independence, Linear Combination, Elementary Matrix

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Basic terminology for systems of equations in a nutshell: l. lady. A system of linear equations is something like the following: Note that the number of equations is not required to be the same as the number of unknowns. A solution to this system would be a set of values for x1 , x2 , and x3 which makes the equations true. For instance, x1 = 3 , x2 = 1 , x3 = 2 is a solution. We will often think of a solution as being a vector: [3, 1, 2] is a solution to the above equation. (for technical reasons, it will later be better to write solution vectors vertically rather than horizontally. For the moment, we won"t worry about the way vectors are written. ) As you know from math 231, a system of two equations can also be thought of as a single equation between two-dimensional vectors.

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