Solutions Manual For Finite Mathematics 7th Edition By
Stefan Waner; Steven Costenoble
3 possible outcomes of a system of 2 linear equations - ANSWER: 1. unique solution
(consistent&independent)
2. infinite solution (dependent)
3. no solution (inconsistent)
methods to solve linear equations - ANSWER: elimination and substitution
In using matrices to solve systems of linear equations, what are the 3 allowed row
operations? - ANSWER: swap any 2 rows, replace a row by a multiple of itself,
replace a row by sum of that row and constant multiple of another row
What is a dependent system? - ANSWER: system with infinitely many solutions
How is the solution of a dependent system expressed? - ANSWER: with an arbitrary
variable (t, f(t))
When we row reduce a matrix, we must always turn each pivot into a 1 before
clearing its column, or else errors will result. - ANSWER: false
Some row reduced matrices have a 0 in the top left-hand corner - ANSWER: true
If the graphs of two linear equations are parallel and distinct, then there is a unique
solution to the system. - ANSWER: False. The system has no solution.
If a system of linear equations has infinitely many solutions, then it may be
inconsistent. - ANSWER: false
The system x + y + z = 1; x = y; y = z, y = 1 is inconsistent. - ANSWER: true
If two of the equations in a system of linear equations are inconsistent, then the
whole system is inconsistent. - ANSWER: true
The system of equations ax + by = 0; cx + dy = 0 has at least one solution regardless
of the values of a, b, c, d. - ANSWER: true
If the row reduced form of a matrix has more than one non-zero entry in any row,
then the corresponding system of linear equations has infinitely many solutions. -
ANSWER: false
If the graphs of two linear equations are not parallel, then there may be no solution
to the system. - ANSWER: false
, If the row reduced form of the augmented matrix corresponding to a system of
linear equations has a row of zeros, then there are infinitely many solutions. -
ANSWER: false
The system x = y; y = z, x = z is inconsistent. - ANSWER: false
If two linear equations have the same graph, then the associated system has
infinitely many solutions. - ANSWER: true
Every system of three linear equations in three unknowns has at least one solution -
ANSWER: false
If the graphs of two linear equations are not parallel, then there is a unique solution
to the system. - ANSWER: true
If two rows of a square matrix are equal, then the matrix is singular. - ANSWER: true
How do you find the singularity of a matrix? - ANSWER: by the determinate (ad-bc)
0=singular
If a system of linear equations is represented by AX = B and A is invertible, then the
system has infinitely many solutions. - ANSWER: false
If defined, a column times a row is always a 1 × 1 matrix - ANSWER: false
If AB = 0, then either A or B is a zero matrix. - ANSWER: false
If the row-reduced form of a matrix is the identity, then the matrix is singular. -
ANSWER: false
If a system of linear equations is represented by AX = B and A is not invertible, then
the system has no solution. - ANSWER: false
If a system of linear equations is represented by AX = B and A is invertible, then the
system has a unique solution. - ANSWER: true
If A is a 2 × 3 matrix and B is a 3 × 2 matrix, then the product AB is defined - ANSWER:
true
Invertible is the opposite of singular - ANSWER: true
If a game has expected value 2, then the row player will gain two points on every
play assuming both players use their optimal mixed strategies. - ANSWER: false
Different saddle points in the same payoff matrix always have the same payoff -
ANSWER: true
Stefan Waner; Steven Costenoble
3 possible outcomes of a system of 2 linear equations - ANSWER: 1. unique solution
(consistent&independent)
2. infinite solution (dependent)
3. no solution (inconsistent)
methods to solve linear equations - ANSWER: elimination and substitution
In using matrices to solve systems of linear equations, what are the 3 allowed row
operations? - ANSWER: swap any 2 rows, replace a row by a multiple of itself,
replace a row by sum of that row and constant multiple of another row
What is a dependent system? - ANSWER: system with infinitely many solutions
How is the solution of a dependent system expressed? - ANSWER: with an arbitrary
variable (t, f(t))
When we row reduce a matrix, we must always turn each pivot into a 1 before
clearing its column, or else errors will result. - ANSWER: false
Some row reduced matrices have a 0 in the top left-hand corner - ANSWER: true
If the graphs of two linear equations are parallel and distinct, then there is a unique
solution to the system. - ANSWER: False. The system has no solution.
If a system of linear equations has infinitely many solutions, then it may be
inconsistent. - ANSWER: false
The system x + y + z = 1; x = y; y = z, y = 1 is inconsistent. - ANSWER: true
If two of the equations in a system of linear equations are inconsistent, then the
whole system is inconsistent. - ANSWER: true
The system of equations ax + by = 0; cx + dy = 0 has at least one solution regardless
of the values of a, b, c, d. - ANSWER: true
If the row reduced form of a matrix has more than one non-zero entry in any row,
then the corresponding system of linear equations has infinitely many solutions. -
ANSWER: false
If the graphs of two linear equations are not parallel, then there may be no solution
to the system. - ANSWER: false
, If the row reduced form of the augmented matrix corresponding to a system of
linear equations has a row of zeros, then there are infinitely many solutions. -
ANSWER: false
The system x = y; y = z, x = z is inconsistent. - ANSWER: false
If two linear equations have the same graph, then the associated system has
infinitely many solutions. - ANSWER: true
Every system of three linear equations in three unknowns has at least one solution -
ANSWER: false
If the graphs of two linear equations are not parallel, then there is a unique solution
to the system. - ANSWER: true
If two rows of a square matrix are equal, then the matrix is singular. - ANSWER: true
How do you find the singularity of a matrix? - ANSWER: by the determinate (ad-bc)
0=singular
If a system of linear equations is represented by AX = B and A is invertible, then the
system has infinitely many solutions. - ANSWER: false
If defined, a column times a row is always a 1 × 1 matrix - ANSWER: false
If AB = 0, then either A or B is a zero matrix. - ANSWER: false
If the row-reduced form of a matrix is the identity, then the matrix is singular. -
ANSWER: false
If a system of linear equations is represented by AX = B and A is not invertible, then
the system has no solution. - ANSWER: false
If a system of linear equations is represented by AX = B and A is invertible, then the
system has a unique solution. - ANSWER: true
If A is a 2 × 3 matrix and B is a 3 × 2 matrix, then the product AB is defined - ANSWER:
true
Invertible is the opposite of singular - ANSWER: true
If a game has expected value 2, then the row player will gain two points on every
play assuming both players use their optimal mixed strategies. - ANSWER: false
Different saddle points in the same payoff matrix always have the same payoff -
ANSWER: true
