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Example36

# Example36 - Example 2 Solve this system of equations using...

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Example 1 Evaluate the following determinant. First find the minor determinants. The solution is To use determinants to solve a system of three equations with three variables (Cramer's Rule), say x , y , and z , four determinants must be formed following this procedure: 1. Write all equations in standard form. 2. Create the denominator determinant, D , by using the coefficients of x , y , and z from the equations and evaluate it. 3. Create the x -numerator determinant, D x , the y -numerator determinant, D y , and the z - numerator determinant, D z , by replacing the respective x , y , and z coefficients with the constants from the equations in standard form and evaluate each determinant. The answers for x , y , and z are as follows:

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Unformatted text preview: Example 2 Solve this system of equations, using Cramer's Rule. Find the minor determinants. Use the constants to replace the x-coefficients. Use the constants to replace the y-coefficients. Use the constants to replace the z-coefficients. Therefore, The check is left to you. The solution is x = 1, y = –2, z = –3. If the denominator determinant, D , has a value of zero, then the system is either inconsistent or dependent. The system is dependent if all the determinants have a value of zero. The system is inconsistent if at least one of the determinants, D x , D y , or D z , has a value not equal to zero and the denominator determinant has a value of zero....
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