Solve a Consistent System of Three Linear Equations with Dependent Equations (Example 4.35)
An example demonstrating how to solve a consistent system of three linear equations with dependent equations, which has infinitely many solutions. Consider the system: Step 1: Eliminate using the first and third equations by multiplying the first by and adding it to the third, yielding . Step 2: Eliminate again using the first and second equations by multiplying the first by and adding it to the second, yielding . Step 3: Eliminate using the two new equations by multiplying the first by and adding it to the second, which results in the true statement . This indicates a dependent system with infinitely many solutions. Solving the first new equation for gives . Substituting this into the original first equation and solving for gives . The solutions are of the form where is any real number.
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Solve a Consistent System of Three Linear Equations with Dependent Equations (Example 4.35)
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Solve a Consistent System of Three Linear Equations with Dependent Equations (Try It 4.69)
Solve a Consistent System of Three Linear Equations with Dependent Equations (Try It 4.70)
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