1.-Consider the system of equations
Does this system have a solution? If so, describe explicitly all solutions.
2.-Give an example of a system of two linear equations in two unknowns which
has no solution.
Thanks so much for your help
1.-Consider the system of equations
Does this system have a solution? If so, describe explicitly all solutions.
2.-Give an example of a system of two linear equations in two unknowns which
has no solution.
Thanks so much for your help
To find out if it has a solution, set it up in matrix form (column form) and reduce to row echelon form. So:
This is the matrix if column form with the augmented solutions. Now if you end up with some row where 0 = a number that isn't 0, there is no solution.
For the second problem:
In this case you know there is no solution since if you were to cancel out by multiplying the top row by and adding the two equations, you get:
Which we know is not true.
It is not necessary to use a matrix form (although that is more "sophisticated" and may well be easier). A more "basic" way to do the first problem is to multiply the first equation, , by 3 to get and subtract the third equation, , from it to eliminate and get . That is identical to the second equation and is equivalent to . Choose any value you want for, say, , use that equation to find and then use either of the other two equations to find .