

Conditions for Consistency in Linear Systems
Interactive Video
•
Mathematics
•
9th - 10th Grade
•
Practice Problem
•
Hard
Thomas White
FREE Resource
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25 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the primary goal of the Gaussian Elimination method?
To find the determinant of a matrix
To perform matrix multiplication
To solve linear systems by transforming them into a triangular form
To calculate eigenvalues of a matrix
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the first case of Gaussian Elimination, what condition must be met for the system to have a unique solution?
The matrix must be diagonal
The last element of the triangular form, tnn, must be zero
The matrix must be symmetric
The last element of the triangular form, tnn, must not be zero
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does it mean if a linear system is consistent?
It has at least one solution
It has no solution
It has a negative determinant
It has exactly two solutions
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the second case of Gaussian Elimination, what is the result if tnn is zero and cnn is not zero?
The system has no solution
The system is symmetric
The system has a unique solution
The system has infinitely many solutions
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the implication of a system being inconsistent?
It has infinitely many solutions
It has no solution
It has a unique solution
It is a diagonal matrix
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the third case of Gaussian Elimination, what happens when both tnn and cnn are zero?
The system is inconsistent
The system has infinitely many solutions
The system has no solution
The system has a unique solution
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why does the third case result in infinitely many solutions?
Because there are more equations than unknowns
Because there are fewer equations than unknowns
Because the matrix is diagonal
Because the determinant is zero
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