To describe: the augmented matrix of a system, elementary row operation, row-echelon form and back-substitution and leading variables.
Answer to Problem 6RCC
The augmented matrix is done by taking the coefficients of the variables appearing in each equation and making them the entries of the matrix
Explanation of Solution
The augmented matrix of a system is a matrix that represents a system of equations. This is done by taking the coefficients of the variables appearing in each equation and making them the entries of the matrix.
On the far left are the values that the equations are set equal.
These equations are of the form
An augmented matrix, perform three elementary row operations:
• addition/subtraction of rows
• multiplication of a row by a nonzero constant
• switching rows
These operations are equivalent to manipulating the equations of a linear system directly. By carrying out these operations in a systematic fashion, obtain the row-echelon form of the matrix which satisfies the following properties:
• The first nonzero entry is called leading entry which is 1
• The leading entry should be the right of the previous leading entry
• At the bottom of the matrix, there will be a row of zeros
The row-echelon form of the augmented matrix of a linear system is easier to solve because use back-substitution to obtain the solution.
By solve for the leading variable in each row, represented by the leading entry of the row, work backwards, row by row, from the bottom of the augmented matrix to solve for the next variable.
This allows us to eventually obtain the solution to the linear system
Chapter 10 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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