Need all of these answered (1-6). This is for my Matrix Algebra class and should be solved as such. Thanks! Underdetermined and Overdetermined Systems of Equations The next system of linear equations is said to be underdetermined because there are more variables than equations. x1 + 2x2 - 3x3 = 4 2x1 - x2 + 4x3 = -3 Similarly, the following system is overdetermined because there are more equations than variables. x1 +3x2 = 5 2x1 - 2x2 = -3 -x1 + 7x2 = 0 You can explore whether the number of variables and the number of equations have any bearing on the consistency of a system of linear equations. For Exercises 1-4, if an answer is yes, give an example. Otherwise, explain why the answer is no. Can you find a consistent underdetermined linear system? Can you find a consistent overdetermined linear system? Can you find an inconsistent underdetermined linear system? Can you find an inconsistent overdetermined linear system? Explain why you would expect an overdetermined linear system to be inconsistent. Must this always be the case? Explain why you would expect an underdetermined linear system to have an infinite number of solutions. Must this always be the case? Solution 1 yes x+y+z=1 x +y-z= 2 2 yes x+y = 4 x-y=2 2x+2y = 8 3 yes x+y+z=4 3x+3y+3z = 12 4yes x+y =4 x-y=2 2x+y = 100 5 Because overdetermined linear system has a equation extra which may or may not satisfy the solutions obtained from the remaining equations. It is not the case that it will always be inconsistent 6 In an undetermimed linear system, one equation is less than the required no. to get the solutions. We can assume one variable constant and find all the solutions w.r.t to that variable.As the value of the constant can take infinite values, we have infinite solutions. It is not the case that it will always have infinite solution as the system can be inconsistent and having no solution. .

1. Need all of these answered (1-6). This is for my Matrix Algebra class and should be solved as
such. Thanks!
Underdetermined and Overdetermined Systems of Equations The next system of linear equations
is said to be underdetermined because there are more variables than equations. x1 + 2x2 - 3x3 =
4 2x1 - x2 + 4x3 = -3 Similarly, the following system is overdetermined because there are more
equations than variables. x1 +3x2 = 5 2x1 - 2x2 = -3 -x1 + 7x2 = 0 You can explore whether the
number of variables and the number of equations have any bearing on the consistency of a
system of linear equations. For Exercises 1-4, if an answer is yes, give an example. Otherwise,
explain why the answer is no. Can you find a consistent underdetermined linear system? Can you
find a consistent overdetermined linear system? Can you find an inconsistent underdetermined
linear system? Can you find an inconsistent overdetermined linear system? Explain why you
would expect an overdetermined linear system to be inconsistent. Must this always be the case?
Explain why you would expect an underdetermined linear system to have an infinite number of
solutions. Must this always be the case?
Solution
1 yes
x+y+z=1
x +y-z= 2
2 yes
x+y = 4
x-y=2
2x+2y = 8
3 yes
x+y+z=4

2. 3x+3y+3z = 12
4yes
x+y =4
x-y=2
2x+y = 100
5
Because overdetermined linear system has a equation extra which may or may not satisfy the
solutions obtained from the remaining equations. It is not the case that it will always be
inconsistent
6
In an undetermimed linear system, one equation is less than the required no. to get the solutions.
We can assume one variable constant and find all the solutions w.r.t to that variable.As the value
of the constant can take infinite values, we have infinite solutions. It is not the case that it will
always have infinite solution as the system can be inconsistent and having no solution.