System of Linear Equations (Solve Using Matrices)

[TheWrathOfMath]

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If both parts are zero then you get [imath]0\cdot w = 0[/imath]. Which values of [imath]w[/imath] would fit this equation?

There are infinitely many values for w, then.

 

[blamocur]

There are infinitely many values for w, then.

Exactly.

 

[TheWrathOfMath]

Exactly.

Okay, and...?

One solution when −α−β≠0
2) No solution when −α−β=0 and −α(β+3)≠0
3) Infinitely many solutions when −α−β=0 and −α(β+3)=0

Is that the answer?

 

[blamocur]

Okay, and...?

One solution when −α−β≠0
2) No solution when −α−β=0 and −α(β+3)≠0
3) Infinitely many solutions when −α−β=0 and −α(β+3)=0

Is that the answer?

This is true for [imath]w[/imath], and haven't yet looked at the other 3 variables -- have you?