To write: the solution of the given system of linear equation.
Answer to Problem 57E
The solution is
Explanation of Solution
Given information:
A system of linear equation is given as
Concept used:
Co-efficient matrix of a system of linear equation of the form
The augmented matrix of the system of linear equation is given by
A matrix is in row-echelon form is
- If any row containing all elements as zero is in the bottom of the matrix.
- Each row that does not consist entirely of zeros has the first nonzero entry as 1.
- For successive nonzero rows the leading 1 in the higher row is further than the leading in the lower row.
And a matrix is in reduced row echelon form if every column that has a leading 1 has zeros in every position above and below its leading 1.
To solve a system of linear equation, the corresponding augmented matrix need to reduce in row echelon form using Gaussian elimination method.
Consider the given system of equation.
Now, the augmented matrix is given by
Now, to solve the system of equation the corresponding augmented matrix need to reduce in row echelon form using Gaussian elimination method.
Multiply row 1 of the matrix by
Apply
Multiply row 2 by
Apply
Multiply row 2 by
Apply
So, the required row echelon formis
The matrix is row reduced augmented matrix by Gauss Elimination method.
Now, the corresponding solution will be
Variables x , y have been used with the coefficients.
Therefore, solution of the system of linear equation is
Chapter 7 Solutions
Precalculus with Limits: A Graphing Approach
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