(a).
Given matrix is in row-echelon form or not.
(a).
Answer to Problem 15E
The given matrix is not 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
But the given matrix has row which consisting entirely zeros is not at the bottom of the matrix.
So the given matrix is not in row-echelon form as it fits into criteria of the row-echelon form properties.
Conclusion:
Thus the given matrix is not in row-echelon form.
(b).
Given matrix is in reduced row-echelon form or not.
(b).
Answer to Problem 15E
The matrix is 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 in reduced row-echelon form.
Conclusion:
Thus the matrix is in reduced row-echelon form.
(c).
System of equations for which given matrix is the argument matrix.
(c).
Answer to Problem 15E
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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