Consider system of equations x + y -az | vedclass

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Question

$\Delta=\left|\begin{array}{ccc}{1} & {1} & {-a} \ {2} & {a} & {1} \ {a} & {1} & {-1}\end{array}ight|=1(-a-1)-1(-2-a)-a\le

Vedclass · Accepted Answer

for $a \in \left\{ {1,\frac{{ - 1 \pm \sqrt 5 }}{2}} \right\}$ , system has no solution.

Vedclass · Answer

$\Delta=\left|\begin{array}{ccc}{1} & {1} & {-a} \ {2} & {a} & {1} \ {a} & {1} & {-1}\end{array}ight|=1(-a-1)-1(-2-a)-a\left(2-a^{2}ight)$

$=a^{3}-2 a+1=(a-1)\left(a^{2}+a-1ight)$

$=(a-1)\left(a-\frac{-1-\sqrt{5}}{2}ight)\left(a-\frac{-1+\sqrt{5}}{2}ight)$

For $\Delta=0$

$a=1, \frac{-1 \pm \sqrt{5}}{2}$

for each value system has no solution.

Consider system of equations $ x + y -az = 1$ ; $2x + ay + z = 1$ ; $ax + y -z = 2$

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