Maths-
General
Easy
Question
If M =
and M2 –
M –
= 0, then
equals -
- –2
- 2
- –4
- 4
The correct answer is: 4
We are given the matrix M and an equation for λ and asked to find the value of λ
![M space equals open square brackets table row 1 2 row 2 3 end table close square brackets
M squared equals open square brackets table row 1 2 row 2 3 end table close square brackets open square brackets table row 1 2 row 2 3 end table close square brackets equals open square brackets table row 5 8 row 8 13 end table close square brackets
M squared minus lambda M minus I space equals space 0
open square brackets table row cell 5 minus lambda minus 1 end cell cell 8 minus 2 lambda end cell row cell 8 minus 2 lambda end cell cell 13 minus 3 lambda minus 1 end cell end table close square brackets equals open square brackets table row 0 0 row 0 0 end table close square brackets
8 minus 2 lambda equals 0
lambda equals 4](data:image/png;base64,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Therefore the correct option is choice 4
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