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Questions and Answers
What is the general form of a linear equation in R2?
What is the general form of a linear equation in R2?
- ax + by = c (correct)
- ax + by + cz = d
- ax^2 + by^2 = c
- ax + by + c = 0
What is the constant term in a linear equation with n variables?
What is the constant term in a linear equation with n variables?
- The last variable in the equation
- The sum of all the coefficients
- The term not associated with any variable (correct)
- The coefficient of the first variable
When is a tuple (s1, s2,...,sn) considered a solution to a linear equation a1x1 + a2x2 +...+ anxn = b?
When is a tuple (s1, s2,...,sn) considered a solution to a linear equation a1x1 + a2x2 +...+ anxn = b?
- When (s1, s2,..., sn) are all equal to 0
- When a1s1 + a2s2 +...+ ansn = b (correct)
- When s1, s2,..., sn are all prime numbers
- When s1 = a1, s2 = a2,..., sn = an and b = 0
What is the possible outcome for a system of linear equations?
What is the possible outcome for a system of linear equations?
What is a system called if it has no solution?
What is a system called if it has no solution?
How many solutions does the system x + y + z = 4, x - y + z = 3 have?
How many solutions does the system x + y + z = 4, x - y + z = 3 have?
What are the solutions to x + y + z = 0 and x - y + z = 1 for any r ∈ R?
What are the solutions to x + y + z = 0 and x - y + z = 1 for any r ∈ R?
What is a matrix called that can be thought of as a table with real number entries?
What is a matrix called that can be thought of as a table with real number entries?
What are two systems of linear equations called if they have the same set of solutions?
What are two systems of linear equations called if they have the same set of solutions?
What is the general form of a linear equation in R3?
What is the general form of a linear equation in R3?
In a linear equation with n variables, what are a1, a2,..., an known as?
In a linear equation with n variables, what are a1, a2,..., an known as?
What is the solution to the system of linear equations x + y + z = 4 and x - y + z = 3?
What is the solution to the system of linear equations x + y + z = 4 and x - y + z = 3?
When is a system of linear equations said to have no solution?
When is a system of linear equations said to have no solution?
Which term is used to describe a system of linear equations in R2 that has at least one solution?
Which term is used to describe a system of linear equations in R2 that has at least one solution?
For the system of equations x + y + z = 4 and x - y + z = 3, what is the number of solutions it has?
For the system of equations x + y + z = 4 and x - y + z = 3, what is the number of solutions it has?
What is the set of solutions to the system x + y + z = 0 and x - y + z = 1 for any r ∈ R called?
What is the set of solutions to the system x + y + z = 0 and x - y + z = 1 for any r ∈ R called?
In the context of matrices, what is the matrix associated with a system of linear equations called?
In the context of matrices, what is the matrix associated with a system of linear equations called?
If two systems of linear equations are equivalent, what can be said about their augmented matrices?
If two systems of linear equations are equivalent, what can be said about their augmented matrices?
What is the term for two straight lines in R2 that do not intersect?
What is the term for two straight lines in R2 that do not intersect?
