Q.

Let M be a 2 × 2 matrix such that M11=12 and M211=10 If x1 and x2 (x1 > x2)  are the two
values of x for which det (M–XI)=0 where I is identity matrix of order 2 then the value of 5x1 + 2x2 is

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answer is 8.

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Detailed Solution

Let m=a    bc    d
ab=1,cd=2a+2b=1,c+2d=0m=1042|mxI|=01-x042-x=0(x2)(x+1)=0x1=+2x2=15x1+2x2

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