Find a matrix X such that 2A + B + X = O, where $straight A equals open square brackets table row cell negative 1 end cell 2 row 3 4 end table close square brackets comma space straight B equals open square brackets table row 3 cell negative 2 end cell row 1 5 end table close square brackets.$

Solution

Here space straight A space equals space open square brackets table row cell negative 1 end cell 2 row 3 4 end table close square brackets space comma space straight B equals open square brackets table row 3 cell negative 2 end cell row 1 5 end table close square brackets

Now 2A + B + X = 0

rightwards double arrow

X= - 2A - B

therefore space space space space space space space space straight X equals negative 2 open square brackets table row cell negative 1 end cell 2 row 3 4 end table close square brackets minus open square brackets table row 3 cell negative 2 end cell row 1 5 end table close square brackets equals open square brackets table row 2 cell negative 4 end cell row cell negative 6 end cell cell negative 8 end cell end table close square brackets plus open square brackets table row cell negative 3 end cell 2 row cell negative 1 end cell cell negative 5 end cell end table close square brackets space space space space space space space space space space space space space space space space space equals space open square brackets table row cell 2 minus 3 end cell cell negative 4 plus 2 end cell row cell negative 6 minus 1 end cell cell negative 8 minus 5 end cell end table close square brackets equals open square brackets table row cell negative 1 end cell cell negative 2 end cell row cell negative 7 end cell cell negative 13 end cell end table close square brackets space space

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