In Exercises 1–4 the given matrix represents an augmented matrix for a linear system. Write the corresponding set of linear equations for the system, and use Gaussian elimination to solve the linear system. Introduce free parameters as necessary.
The solution of the system corresponding to the augmented matrix
Answer to Problem 1SE
The solution of the system corresponding to the augmented matrix
Explanation of Solution
The given augmented matrix is
Reduce the matrix
Multiply the first row by
Add
Multiply the second row of the matrix by
The above matrix is in row echelon form.
The corresponding linear system of the row echelon matrix is,
Here
Now assign arbitrary values s, t (called parameter) to
Obtain the value of
Therefore, the solution of the corresponding to the augmented matrix
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Elementary Linear Algebra: Applications Version
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- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning