19 Questions
What is the general form of a linear equation in R2?
ax + by = c
What is the constant term in a linear equation with n variables?
The term not associated with any variable
When is a tuple (s1, s2,...,sn) considered a solution to a linear equation a1x1 + a2x2 +...+ anxn = b?
When a1s1 + a2s2 +...+ ansn = b
What is the possible outcome for a system of linear equations?
It may have no solution, a unique solution, or an infinite family of solutions
What is a system called if it has no solution?
Inconsistent
How many solutions does the system x + y + z = 4, x - y + z = 3 have?
Infinitely many solutions
What are the solutions to x + y + z = 0 and x - y + z = 1 for any r ∈ R?
x = 1/2 - r, y = -1/2, z = r
What is a matrix called that can be thought of as a table with real number entries?
Augmented matrix
What are two systems of linear equations called if they have the same set of solutions?
Equivalent
What is the general form of a linear equation in R3?
$ax + by + cz = d$
In a linear equation with n variables, what are a1, a2,..., an known as?
Coefficients
What is the solution to the system of linear equations x + y + z = 4 and x - y + z = 3?
(2, 2, 0)
When is a system of linear equations said to have no solution?
When it contradicts itself
Which term is used to describe a system of linear equations in R2 that has at least one solution?
Consistent
For the system of equations x + y + z = 4 and x - y + z = 3, what is the number of solutions it has?
Infinitely many
What is the set of solutions to the system x + y + z = 0 and x - y + z = 1 for any r ∈ R called?
Parametric solutions
In the context of matrices, what is the matrix associated with a system of linear equations called?
Augmented matrix
If two systems of linear equations are equivalent, what can be said about their augmented matrices?
They are identical
What is the term for two straight lines in R2 that do not intersect?
Parallel
Test your understanding of systems of linear equations, the form of linear equations, and the variables involved in them. This quiz covers topics such as the equation of a straight line in R2, linear equations with n variables, and constant terms.
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