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| a system of linear equations that has at least one solution or infinitely many |
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| a system of linear equations that has no solution |
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| any zero is listed last, in each nonzero row the first nonzero entry is a 1, or given 2 successive nonzero rows the leading 1 of the first is to the left of the leading 1 of the second |
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| matrix must be in row echelon form and every leading 1 has zeros above and below. |
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| used to solve a matrix by back substitution if it is in row-echelon form |
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| used to solve a matrix by back substitution if it is in reduced row-echelon form |
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| in n variables is an expression of the form ax=b where a,b are fixed real numbers and x is a real variable |
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| an assignment of real numbers such that when substituted for the variables in the equation give a true equality among real numbers |
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| is the set of all solutions to a linear equation |
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| System of Linear Equations |
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| is a collection of m equations each linear in the same n variables. |
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| variable, In algebra, a symbol (usually a letter) standing in for an unknown numerical value in an equation. Commonly used variables include x and y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s (arc length) |
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| A coefficient is any number that is being multiplied to a variable. The variable is the unknown symbol while the number being multiplied to it is called the coefficient. Any variable on its own is said to have one as its coefficient |
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| A fixed and well-defined number or other non-changing mathematical object |
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| two matrices that can be transformed into the other by infinitely many elementary row operations. |
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