Linear Algebra, forcing a row exchange.

[Terrell]

the answer key said d is supposed to be 10. but there's a way to evade that row exchange. 1st picture is the question and the 2nd picture is the elimination steps.

 

[FactChecker]

I think that the question is asking which value of d "forces" a row exchange if you keep it upper triangular. In general, the system of equations can be solved in many ways if you don't insist on keeping an upper triangular form.

 

[Terrell]

I think that the question is asking which value of d "forces" a row exchange if you keep it upper triangular. In general, the system of equations can be solved in many ways if you don't insist on keeping an upper triangular form.

good point!