Problem 69 - Algebra and Trigonometry

Question

Determine whether each statement makes sense or does not make sense, and explain your reasoning. When using Cramer's Rule to solve a linear system, the number of determinants that I set up and evaluate is the same as the number of variables in the system.

Step-by-Step Solution

Answer

The statement makes sense. According to Cramer's Rule, the number of determinants evaluated corresponds to the number of variables in the system.

Step 1 - Reiterate Cramer's Rule

Cramer's Rule is a technique used to systematically solve system of linear equations. For this, you create and evaluate a certain number of determinants. These determinants are created by replacing the coefficients of each variable in the system, one at a time, with the constants from the other side of the equation while keeping the other columns in the determinant unchanged. This process is repeated for each variable in the system. Therefore, for a system with 'n' variables, 'n' determinants are created and evaluated.

Step 2 - Analyze the Statement

The statement indicates that the number of determinants set up and evaluated when using Cramer's Rule to solve a linear system equals the number of variables in the system. Considering the process described in Step 1, it is clear that this statement accurately represents the application of Cramer's Rule.