Question 1 which of the statements below is not true? A. A linear independent se

Question

Question 1 which of the statements below is not true? A. A linear independent set of vectors in R" can be expanded into a basis for R" by adding, if needed, some vectors from the standard basis for R". The row space of a matrix A is a set of all linear combinations of rows of A The row space of an m × n matrix A is a subspace of Rn If two matrices A and B are row equivalent, then their row spaces are the same. A basis for Row A is the set of rows in A which correspond to the nonzero rows in an echelon B of A B. b. E.

Explanation / Answer

A) it is true . It is the theorem

B)It is false . as for example : {(1,2,3),(2,4,6),(1,7,-2)} .u=(1,2,3),v=(2,4,6),w=(1,7,-2).

and linear combination is -2*u+1*v+0*w=0 but {u,v,w} is not row space .

C) It is true . It is theorem

D) It is also true , if two A, B are equivalent then row space same , rank same etc

E) It is true .It is also theorem

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