1. Matrix - Gauss-Jordan

For which values of ( a ) will the system of equations

x+y=0

x+2y+(a+3)z=0

x+y+(a+1)z=a^2 - 1 ( a square minus 1 )

has :

1 - A unique non-zero solution
2- No Solution
3- A trivial solution
4- infinitely many solutions

please i need a little bit of explanation on that

2. Originally Posted by 7amooood
For which values of ( a ) will the system of equations

x+y=0
x+2y+(a+3)z=0
x+y+(a+1)z=a^2 - 1

has :

1 - A unique non-zero solution
2- No Solution
3- A trivial solution
4- infinitely many solutions
Use what you've learned about solving systems of linear equations:

For a system to have infinitely-many solutions, one of the lines in the system has to turn into all zeroes, after a sufficient number of row operations.

For a system to have no solution, one of the lines has to reduce to something non-sensical, like "2 = 0".

For a unique solution, you have to get single numerical values for each of x, y, and z.

(I don't know how your book is defining a "trivial" solution in this context, but it might mean "everything is zero".)

So do the row operations, trying to get the system into row-echelon or reduced-row-echelon form, and see where that leads!

3. Thanks

Thank you very much that helped me so much and i was able to figure out the answer for the question