csat-suneung 2012 Q29

csat-suneung · South-Korea · csat__math-humanities 4 marks Matrices Linear System and Inverse Existence
A $2 \times 2$ square matrix $A$ satisfies the following conditions. (where $E$ is the identity matrix and $O$ is the zero matrix)
(A) $A ^ { 2 } + 2 A - E = O$
(B) $A \binom { 1 } { - 1 } = \binom { 3 } { 4 }$ Find the value of $x + y$ for real numbers $x , y$ satisfying $( A + 2 E ) \binom { x } { y } = \binom { 3 } { - 3 }$. [4 points] 
A $2 \times 2$ square matrix $A$ satisfies the following conditions. (where $E$ is the identity matrix and $O$ is the zero matrix)\\
(A) $A ^ { 2 } + 2 A - E = O$\\
(B) $A \binom { 1 } { - 1 } = \binom { 3 } { 4 }$\\
Find the value of $x + y$ for real numbers $x , y$ satisfying $( A + 2 E ) \binom { x } { y } = \binom { 3 } { - 3 }$. [4 points]
Paper Questions
Q1 Q2 Q3 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 Q21 Q22 Q23 Q24 Q25 Q26 Q27 Q28 Q29 Q30