. Investigate the values of  and  such that the system of equations

Question

x + y + z = 6
x + 2y + 3z = 10
x + 2y + z = , may have

(i) Unique solution

Answer 1

(i)
For the system
x + y + z = 6
x + 2y + 3z = 10
x + 2y + Hz = K
to have unique solution, the determinant on the left hand side, namely
|1 1 1|
|1 2 3| = Δ
|1 2 H|
must be non-zero.
Δ would be zero is when there are two identical rows or columns. This can happen for one value of H.

You will need to stipulate the condition on H such that identical rows do not appear in Δ.

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