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Matrices

Question
CBSEENMA12033028
Wired Faculty App

Evaluate

If A = open square brackets table row 2 cell negative 1 end cell row 3 2 end table close square brackets comma space B equals open square brackets table row 0 4 row cell negative 1 end cell 7 end table close square brackets comma space find space 3 straight A squared minus 2 straight B plus straight I.

Solution
Here space space space space straight A equals space open square brackets table row bold 2 cell bold minus bold 1 end cell row bold 3 bold 2 end table close square brackets bold comma bold space bold B bold equals open square brackets table row bold 0 bold 4 row cell bold minus bold 1 end cell bold 7 end table close square brackets bold space bold therefore bold space bold space bold A to the power of bold 2 bold space bold equals bold space open square brackets table row bold 2 cell bold minus bold 1 end cell row bold 3 bold 2 end table close square brackets bold space bold equals open square brackets table row cell bold 4 bold minus bold 3 end cell cell bold minus bold 2 bold minus bold 2 end cell row cell bold 6 bold plus bold 6 end cell cell bold minus bold 3 bold plus bold 4 end cell end table close square brackets bold equals open square brackets table row bold 1 cell bold minus bold 4 end cell row bold 12 bold 1 end table close square brackets bold Consider bold space bold space bold 3 bold space bold A to the power of bold 2 bold minus bold 2 bold B bold plus bold I bold equals bold 3 bold space open square brackets table row bold 1 cell bold minus bold 4 end cell row bold 12 bold 1 end table close square brackets bold minus bold 2 open square brackets table row bold 0 bold 4 row cell bold minus bold 1 end cell bold 7 end table close square brackets bold plus open square brackets table row bold 1 bold 0 row bold 0 bold 1 end table close square brackets bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold equals open square brackets table row bold 3 cell bold minus bold 12 end cell row bold 36 bold 3 end table close square brackets bold plus open square brackets table row bold 0 cell bold minus bold 8 end cell row bold 2 cell bold minus bold 14 end cell end table close square brackets bold plus open square brackets table row bold 1 bold 0 row bold 0 bold 1 end table close square brackets bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold equals bold space open square brackets table row cell bold 3 bold plus bold 0 bold plus bold 1 end cell cell bold minus bold 12 bold minus bold 8 bold plus bold 0 end cell row cell bold 36 bold plus bold 2 bold plus bold 0 end cell cell bold 3 bold minus bold 14 bold plus bold 1 end cell end table close square brackets bold equals open square brackets table row bold 4 cell bold minus bold 20 end cell row bold 38 cell bold minus bold 10 end cell end table close square brackets

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