Please check my provided answers, unanswered questions I need help with. 1. What
ID: 2861778 • Letter: P
Question
Please check my provided answers, unanswered questions I need help with.
1. What is the significance of a square matrix having a non-zero determinant?
The column vectors and row vectors are independant.
The system of linear equations have a unique solution.
If the system of linear equations are homogenious, the solution is the zero solution.
2. What other conditions are equivalent to this?
3. What are the possible numbers of solutions of a general linear system?
Either no solution, one solution or infinitely many solutions.
4. What are the possible numbers of solutions of a homogeneous linear system?
Either one solution (which is the zero solution) or infinitely many solutions.
5. How can we determine which "number of solutions" applies to a particular problem?
Compute the augmented Row Echelon Form, check for consistency. If the matrix is inconsistent, there is no solution.
Once we know the matrix is consistent, compute the determinate.
Explanation / Answer
(1)
Correct explanation
(2)
Conditions for a square matrix having a non-zero determinant
(a)No rows and no columns should have same values
(b)No rows and no columns will be scalar multiple of other row or other column
(c) No row and no columns will be additions or subtraction of other rows and columns
(3)
Perfect explanation
(4)
Good explanation
(5)
correct explanation