$\"\"$

Consider the $\"\"$ by $\"\"$ matrix is $\"\"$ .

Multiply the each entry in row $\"\"$ of a $\"\"$ by $\"\"$ matrix by the number $\"\"$ .

The determinant is $\"\"$ .

Show that the value of the new determinant is $\"\"$ times the value of the original determinant.

$\"\"$

$\"\"$ .

Therefore, the value of the new determinant is $\"\"$ times the value of the original determinant.

$\"\"$

The value of the new determinant is $\"\"$ times the value of the original determinant.