Question

Each equation in Exercises 1-4 illustrates a property of determinants. State the property

\(\left| {\begin{array}{*{20}{c}}{\bf{1}}&{\bf{3}}&{ - {\bf{4}}}\\{\bf{2}}&{\bf{0}}&{ - {\bf{3}}}\\{\bf{3}}&{ - {\bf{5}}}&{\bf{2}}\end{array}} \right| = \left| {\begin{array}{*{20}{c}}{\bf{1}}&{\bf{3}}&{ - {\bf{4}}}\\{\bf{0}}&{ - {\bf{6}}}&{\bf{5}}\\{\bf{3}}&{ - {\bf{5}}}&{\bf{2}}\end{array}} \right|\)

Short answer

The row operation does not change the value of the determinant.

Step-by-step solution

Recall the property of the determinant

When the row operation is applied to the determinant, its value does not change.

Apply the property for the given determinants

For the determinants, row operation is applied on row 3, i.e., \({R_2} \to {R_2} - 2{R_1}\).

So, the row operation does not change the value of the determinant.