
(a).
Given matrix is in row-echelon form or not.
(a).

Answer to Problem 12E
The given matrix is in row-echelon form.
Explanation of Solution
Given:
Given matrix:
Concept Used:
Properties of row-echelon form.
Calculation:
The first non-zero number in each row is
Also the given matrix has row which consisting entirely zeros is at the bottom of the matrix.
So the given matrix is in row-echelon form as it fits into criteria of the row-echelon form properties.
Conclusion:
Thus the given matrix is in row-echelon form.
(b).
Given matrix is in reduced row-echelon form or not.
(b).

Answer to Problem 12E
The matrix is not in reduced row-echelon form.
Explanation of Solution
Given:
Given matrix:
Concept Used:
Properties of reduced row-echelon form.
Calculation:
Given matrix is as below:
The leading
Therefore, the matrix is not in reduced row-echelon form.
Conclusion:
Thus the matrix is not in reduced row-echelon form.
(c).
System of equations for which given matrix is the argument matrix.
(c).

Answer to Problem 12E
system of equations for the given matrix is:
Explanation of Solution
Given:
Given matrix:
Calculation:
Given matrix is as below:
So the system of equations are:
Thus, equations will be:
Conclusion:
Thus system of equations for the given matrix is as above.
Chapter 10 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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