ICSE Class X Math 2016 Solved Paper - Question 2 | ExamSiri

ICSE Class X Math 2016 Solved Paper

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Question : 2 of 57

Marks: +1, -0

Given

A={[\table 2 , 0 ; -1 , 7]}

and

I={[\table 1 , 0 ; 0 , 1]}

and

A^2=

9 A+m I

. Find

m

.

Solution:

Given :

A={[\table 2 , 0 ; -1 , 7]}

and

I={[\table 1 , 0 ; 0 , 1]}

\; {\A}^2= {\A} ⋅ {\A}={[\table 2 , 0 ; -1 , 7 ]}{[\table 2 , 0 ; -1 , 7 ]}

\;\; ={[\table 4 , 0 ; -2-7 , 0+49 ]}

\;\; ={[\table 4 , 0 ; -9 , 49 ]}

\;9 {\A}+m {\I}=9{[\table 2 , 0 ; -1 , 7 ]}+m{[\table 1 , 0 ; 0 , 1 ]}

= {[\table 18 , 0 ; -9 , 63 ]}+{[\table m , 0 ; 0 , m ]}

\;\; ={[\table 18+m , 0 ; -9 , 63+m ]}

Now, According to question,

{\A}^2\;=9 {\A}+m {\I}

{{[\table 4 , 0 ; -9 , 49 ]} }\;={[\table 18+m , 0 ; -9 , 63+m ]}

comparing both sides,

4\;=18+m \;\text " and "\; 49=63+m

⇒

m\;=-14

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