Term
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Definition
A matrix is in row-echelon form if:
(a) All rows that contain only zeros are grouped at the bottom of the matrix.
(b) for each row that does not contain only zeros, the pivot appears strictly to the right of the pivot of each row that appears above it. |
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Term
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Definition
| Let e be an elementary row operation. The the n x n matrix elementary matrix E associated with e is the matrix obtained by applying e to the n x n identity matrix. Thus E=e(I) |
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Term
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Definition
| Let A b an m x n matrix. The set {xis an element of R^n where Ax=0} is called the null sace of A and is denoted by NS(A). |
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Term
| subspace of a vector space |
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Definition
| A nonempty subset S of a vector space V is called a subspace of V is S is closed under addition and scalar multiplication so that all axioms of a vector space are satisfied. |
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Term
| a vector is a linear combination when |
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Definition
| A vector w is called a linear combination of the vectors vsub1,...,vsubk i there ar numbers asub1,...,asubk such that w=asub1vsub1+...+asubkvsubk |
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Term
| basis for a vector space V is |
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Definition
a subspace S that
1)is linearly independent
2)spans the vector space v |
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Term
| dimension of a vector space |
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Definition
| is n (a positive vector) if V has a basis of n elements. |
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