I am having difficulty with true/false statements and their justifications regarding systems of linear equations.(a) A linear system of three equations in five unknowns is always consistent (i.e. it has at least one solution)(b) A linear system of five equations in three unknowns cannot be consistent(c) If a linear system in echelon form is triangular then the system has the unique solution(d) If a linear system of n equations in n unknowns has two equations that are multiples of one another, then the system is inconsistent.So far, for (a) I have said False, as it will always be consistent if it is homogeneous, but not if it is non-homogeneous.For (b) I have said false, but am having difficulty justifying this assertionc) I know to be true.(d) I believe may be false as having equations that are multiples could result in free variables and hence infinite solutions?I am rather unsure on what I have done so far.Any assistance is greatly appreciated.

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zuiverevv03m · Accepted Answer

for part b , you may consider below counter example:      x    1    +      x    2    +      x    3    =  1for part d:you&#039;re correct about the answer but your reasoning is only partially correct - the system can also be inconsistent:      x    1    +      x    2    +      x    3    =  1  2      x    1    +  2      x    2    +  2      x    3    =  2      x    1    +      x    2    +      x    3    =  2

Jabari Pitts · Accepted Answer

for part(1), I can give one example a+b+c+d+e=1,2a+b+c+d+e=2,3a+b+c+d+e=5, this system of three equations in 5 variables has no solution or it is inconsistent.Hence the given statement is false. for part(2), we can have one example a+b+c=3, 2a+2b+c=5, 2a+b+2c=5, a+2b+2c=5, a+b+2c=4. This is a system of five equations in 3 variables with solution a=b=c=1. Hence the given statement is false.

I am having difficulty with true/false statements and their justifications regarding systems of line

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