4 For each of the following statements either prove that the

4) For each of the following statements, either prove that the statement is true, or find an example that shows the statement is false:

a) If A is an n × n matrix whose columns are linearly dependent, then the rows of A are also linearly dependent.

b) If A is an n × n matrix whose rows are linearly dependent, then the columns of A are also linearly dependent.

Solution

if column/raw is linearly dependent determinant will be 0. it det is 0 then vectors forming determinant are linearly dpendent . so raw/column will be dependent too.