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  • Elementary matrices

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  • A nonsingular matrix can be written as a product of elementary matrices.
  • Row operations are given by multiplication by elementary matrices.
  • Elementary matrices are invertible/nonsingular.
  • Definition of elementary matrix
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  1. Definition of elementary matrix

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  • Elementary matricesClose match
  • Row operations are given by multiplication by elementary matrices.Close match
  • Elementary matrices are invertible/nonsingular.Close match
  • Theorem describing the determinants of elementary matrices.Close match
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  • A nonsingular matrix can be written as a product of elementary matrices.Close match
  • Definition of identity matrixClose match
  • Definition of unit matrixClose match
  • Definition of the determinant in terms of the effect of elementary row operationsClose match
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  • Definition of square matrixClose match
  • Operations on matricesClose match
  • Definition of (echelon matrix/matrix in (row) echelon form)Close match
  • Definition of m by n matrixClose match
  • Echelon matricesClose match
  • Definition of (row) echelon form of a matrixClose match
  • Example of putting a matrix in echelon formClose match
  • Row-equivalent augmented matrices represent equivalent systemsClose match

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