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 whichThanks so much for your help

has no solution.

- Aug 26th 2009, 09:40 PMosodudTwo difficult linear algebra exercises (systems of equations)
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*Thanks so much for your help

has no solution.

- Aug 26th 2009, 10:03 PMeXist
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. - Aug 27th 2009, 04:52 AMHallsofIvy
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 .