csat-suneung 2007 Q30

csat-suneung · South-Korea · csat__math-humanities 4 marks Matrices Determinant and Rank Computation

For a $2 \times 2$ square matrix $X = \left( \begin{array} { l l } a & b \\ c & d \end{array} \right)$, $$D ( X ) = a d - b c$$ is defined. For a $2 \times 2$ square matrix $A = \left( \begin{array} { l l } 1 & 1 \\ 0 & p \end{array} \right)$, $$D \left( A ^ { 2 } \right) = D ( 5 A )$$ Find the sum of all constants $p$ that satisfy this condition. [4 points]

For a $2 \times 2$ square matrix $X = \left( \begin{array} { l l } a & b \\ c & d \end{array} \right)$,
$$D ( X ) = a d - b c$$
is defined. For a $2 \times 2$ square matrix $A = \left( \begin{array} { l l } 1 & 1 \\ 0 & p \end{array} \right)$,
$$D \left( A ^ { 2 } \right) = D ( 5 A )$$
Find the sum of all constants $p$ that satisfy this condition. [4 points]

Paper Questions

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