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Found in: Page 165

### Linear Algebra and its Applications

Book edition 5th
Author(s) David C. Lay, Steven R. Lay and Judi J. McDonald
Pages 483 pages
ISBN 978-03219822384

# Each equation in Exercises 1-4 illustrates a property of determinants. State the property$$\left| {\begin{array}{*{20}{c}}{\bf{1}}&{\bf{3}}&{ - {\bf{4}}}\\{\bf{2}}&{\bf{0}}&{ - {\bf{3}}}\\{\bf{3}}&{ - {\bf{5}}}&{\bf{2}}\end{array}} \right| = \left| {\begin{array}{*{20}{c}}{\bf{1}}&{\bf{3}}&{ - {\bf{4}}}\\{\bf{0}}&{ - {\bf{6}}}&{\bf{5}}\\{\bf{3}}&{ - {\bf{5}}}&{\bf{2}}\end{array}} \right|$$

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

See the step by step solution

## Step 1: Recall the property of the determinant

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

## Step 2: 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.