Chapters
Exercise 1
Solve:
Exercise 2
Solve:
Exercise 3
Solve:
Exercise 4
Consider the following system for different values of a and b:
Exercise 5
Solve:
Exercise 6
Consider the following system for different values of a and b:
Exercise 7
Determine for what values of k, the following system has infinite solutions:
Exercise 8
Solve:
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Solution of exercise 1
Solve:
If a=, r(A) = r(A')=2, n=3
If , this means that the system is a consistent independent system!
Solution of exercise 2
Solve:
Supposing :
, this means that the system is a consistent dependent system!
, supposing
In case, , this means that the system is a consistent independent system!
Solution of exercise 3
Solve:
If
, this means that the system is an inconsistent system!
If this means that the system is a consistent independent system!
Applying row operation :
Solution of exercise 4
Consider the following system for different values of a and b:
, this means that the system is a consistent independent system!
If :
, this means that the system is an Inconsistent system!
Otherwise, this means that the system is a consistent dependent system!
If :
, this means that the system is an Inconsistent system!
Solution of exercise 5
Solve:
We will be using row operations:
Finding the value of a from the 3rd row:
In the third row, means that the system is a consistent dependent system.
which means inconsistent system.
Solution of exercise 6
Consider the following system for different values of a and b:
Applying these row operations:
, hence it is a consistent indendent system
which indicates that the system is an inconsistent system
which indicates that the system is a consistent dependent system
Solution of exercise 7
Determine for what values of k, the following system has infinite solutions:
Applying row operations:
* 2 was taken as common and divided by 0
Solution of exercise 8
Solve:
Applying these row operations:
, this means that the system is an inconsistent system (for any value of m)
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very nice explanation. it is understandable.