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13 Cards in this Set
- Front
- Back
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How to name a matrix |
Number of rows x number of columns |
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Elementary Row Operations |
Replacement, Scaling, interchange |
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Row reduction |
Process to transform a matrix using elementary row operations to (reduced) echelon form |
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Echelon Form |
Each first row entry has all zeroes underneath, all zero rows are below all others |
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Reduced Echelon form |
Each first row entry is a one, and is the only entry in that column that is a number other than zero. All zero rows are below all others |
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Pivot Entry |
a position in a matrix that corresponds to a leading entry in the matrix in (reduced) echelon form |
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Basic Variable |
A variable who's column has a pivot entry |
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Free variable |
A variable that is not basic. There is no pivot entry in the column |
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Possible solutions to a system of linear equations |
No solution, one solution, infinitely many solutions |
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When is a matrix consistant |
no equation with the form "0=b" |
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When does a system of equations have no solution |
It is not consistent, has an equation in the form, "0=b" |
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When does a system of equations have only one solution? |
It is consistent and has no free variables |
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When does a system of equations have infinitely many solutions? |
It is consistent and has at least one free variable |
