(a)
To explain: whether the system has exactly one solution or not
(a)
Answer to Problem 8RCC
Each variable in the row-echelon form should be a leading variable.
Explanation of Solution
Calculation:
A linear system of equations has exactly one solution.
If each variable in the row-echelon form of the augmented matrix is a leading variable.
That is, there are exactly as many nonzero leading entries as there are variables in the system of equations.
(b)
To explain: whether the system hasno solution or not
(b)
Answer to Problem 8RCC
A matrix contains a row of zeros, except for the last entry in that row on the far right.
Explanation of Solution
Calculation:
A linear system of equations has no solution if the system is inconsistent.
This means that the row-echelon form of its augmented matrix contains a row of zeros, except for the last entry in that row on the far right.
Such a row represents the equation
(c)
To explain: whether the system hasinfinitely many solutionor not
(c)
Answer to Problem 8RCC
Each variable in the row-echelon form should not be a leading variable.
Explanation of Solution
Calculation:
A linear system of equations has infinitely many solutions.
If each variable in the row-echelon form of the augmented matrix is not a leading variable.
That is, there are more variables than there are nonzero leading entries. Furthermore, the system cannot be inconsistent - it cannot contain a row that represents the equation
Chapter 10 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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