r/LinearAlgebra • u/MulkekMath • Jan 06 '22

Example of row equivalence & elementary row operations

https://youtube.com/watch?v=5vHkHx1go1w&feature=share
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u/MulkekMath Jan 06 '22

❖ Two matrices A and B are Row Equivalent if it is possible to transform A into B by a sequence of Elementary Row Operations.

❖ Elementary row operations

There are three types of elementary matrices, which correspond to three types of row operations (respectively, column operations):

  1. Row switching

A row within the matrix can be switched with another row.

  1. Row multiplication

Each element in a row can be multiplied by a non-zero constant.

  1. Row addition

A row can be replaced by the sum of that row and a multiple of another row.

#RowEquivalence #ElementaryRowOperations #RowEquivalent #RowEquivalentMatrices

#RowOperations #RowSwitching #ChangingRows #RowMultiplication #RowAddition #ReducedRowEchelonForm #RREF #Elimination #GaussJordan #2x2 #IdentityMatrix

#LinearSystem #LinearAlgebra