7.4 Linear Independence. Rank of a Matrix

A={{3,0,2,2},{-6,42,24,54},{21,-21,0,-15}}

MatrixForm[A]

MatrixRank[A]

A[[1]]

6 A[[1]] - 0.5 A[[2]]

6 A[[1]] - 0.5 A[[2]]==A[[3]]

RowReduce[A]

MatrixForm[%]

A={{8,2,5},{16,6,29},{4,0,-7}}

MatrixForm[A]

MatrixRank[A]

3 A[[1]]-2 A[[3]]

A={{0,3,4},{-3,0,-5},{-4,5,0}}

MatrixForm[A]

MatrixRank[A]

RowReduce[A]

5/3 A[[1]]+4/3 A[[2]]

A={{0,1,2},{3,4,5},{1,0,1}}

MatrixRank[A]

RowReduce[A]

B=Transpose[A]

MatrixForm[B]

MatrixRank[B]

B={{1,1,a},{1,a,1},{a,1,1}}

MatrixForm[B]

MatrixRank[B]

RowReduce[B]