TS ICET 2015 Question Paper with Solutions for online practice

Question : 138 of 200

Marks: +1, -0

A =

[\table\1, 2 ,2; 2, 1, 2; 2, 2, 1]

⇒

A^2

- 4A =

Solution:

A=[\table\1, 2 ,2; 2, 1, 2; 2, 2, 1]

∴A^2=[\table1,2,2; 2, 1, 2; 2, 2, 1][\table1,2,2; 2, 1, 2; 2, 2, 1],A4=4[\table1,2,2; 2, 1, 2; 2, 2, 1]

=[\table;1+4+4,2+2+4,2+4+2;2+2+4,4+1+4,4+2+2;2+4+2,4+2+2,4+4+1]=[\table9,8,8;8,9,8;8,8,9]

⇒A^2-4A=[\table9,8,8;8,9,8;8,8,9]-[\table4,8,8;8,4,8;8,8,4]

=[\table5,0,0;0,5,0;0,0,5]=5[\table1,0,0;0,1,0;0,0,1]=5I

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