csat-suneung 2016 Q24

csat-suneung · South-Korea · csat__math-A 3 marks Invariant lines and eigenvalues and vectors Compute eigenvectors or eigenspaces

For the system of linear equations in $x , y$ $$\left( \begin{array} { c c } 1 & a - 2 \\ 2 & - 1 \end{array} \right) \binom { x } { y } = 3 \binom { x } { y }$$ Find the value of the constant $a$ such that the system has a solution other than $x = 0 , y = 0$. [3 points]

For the system of linear equations in $x , y$
$$\left( \begin{array} { c c } 1 & a - 2 \\ 2 & - 1 \end{array} \right) \binom { x } { y } = 3 \binom { x } { y }$$
Find the value of the constant $a$ such that the system has a solution other than $x = 0 , y = 0$. [3 points]

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