Math 225 stuvia - Study guides, Class notes & Summaries

The Invertible Matrix Theorem - Answer Let A be a square nxn matrix. Then the following statements are equivalent. All are true or all are false: a.) A is an invertible matrix b.) A is row equivalent to the nxn identity matrix c.) A has n pivot positions d.) the equation Ax=0 has only the trivial solution e.) the columns of A form a linearly independent set f.) the linear transformation x→Ax is one-to-one g.) the equation Ax=b has at least one solution for each b in Rⁿ h.) the column...

Finding a parametric description of the solution set of a linear system is the same as solving the system. Is this statement true or​ false? - Answer The statement is false. The solution set of a linear system can only be expressed using a parametric description if the system has at least one solution. If one row in an echelon form of an augmented matrix is [ 0 0 0 5 0 ] then the associated linear system is inconsistent. Is this statement true or​ false? - Answer The statement is fals...