Question

$Given space that space straight A equals space open square brackets table row 1 cell negative 1 end cell cell space space 0 end cell row cell 2 space end cell cell space space space 3 end cell cell space space space 4 end cell row 0 cell space space 1 end cell cell space space 2 end cell end table close square brackets space and space straight B equals space open square brackets table row 2 cell space space space 2 end cell cell negative 4 end cell row cell negative 4 end cell cell space space 2 end cell cell space space minus 4 end cell row 2 cell negative 1 end cell 5 end table close square brackets space Find space AB space space Use space to space solve space the space following space system space of space equations space straight x space minus space straight y space equals space 3 comma space 2 straight x space plus space 3 straight y space plus space 4 straight z space equals space 17 comma space straight y space plus space 2 straight z space equals space straight l.$

Solution

straight A equals space open square brackets table row 1 cell negative 1 end cell cell space space 0 end cell row cell 2 space end cell cell space space space 3 end cell cell space space space 4 end cell row 0 cell space space 1 end cell cell space space 2 end cell end table close square brackets space and space straight B equals space open square brackets table row 2 cell space space space 2 end cell cell negative 4 end cell row cell negative 4 end cell cell space space 2 end cell cell space space minus 4 end cell row 2 cell negative 1 end cell 5 end table close square brackets AB equals space open square brackets table row 1 cell negative 1 end cell cell space space 0 end cell row cell 2 space end cell cell space space space 3 end cell cell space space space 4 end cell row 0 cell space space 1 end cell cell space space 2 end cell end table close square brackets space open square brackets table row 2 cell space space space 2 end cell cell negative 4 end cell row cell negative 4 end cell cell space space 2 end cell cell space space minus 4 end cell row 2 cell negative 1 end cell 5 end table close square brackets space space space space space equals space open square brackets table row cell 2 plus 4 plus 0 end cell cell space space space 2 minus 2 plus 0 end cell cell negative 4 plus 4 plus 0 end cell row cell 4 minus 12 plus 8 end cell cell space space space 4 plus 6 minus 4 end cell cell space space space minus 8 minus 12 plus 20 end cell row cell 0 minus 4 plus 4 end cell cell space space 0 plus 2 minus 2 end cell cell 0 minus 4 plus 10 end cell end table close square brackets space space equals space open square brackets table row cell 6 space end cell cell space space 0 end cell cell space space 0 end cell row 0 cell space space 6 end cell cell space space space 0 end cell row 0 cell space space 0 end cell cell space space 6 end cell end table close square brackets therefore space space AB equals space open square brackets table row cell 6 space end cell cell space space 0 end cell cell space space 0 end cell row 0 cell space space 6 end cell cell space space space 0 end cell row 0 cell space space 0 end cell cell space space 6 end cell end table close square brackets space space space space space space space space space.... left parenthesis 1 right parenthesis Again space space BA equals space open square brackets table row 2 cell space space space 2 end cell cell negative 4 end cell row cell negative 4 end cell cell space space 2 end cell cell space space minus 4 end cell row 2 cell negative 1 end cell 5 end table close square brackets space space open square brackets table row 1 cell negative 1 end cell cell space space 0 end cell row cell 2 space end cell cell space space space 3 end cell cell space space space 4 end cell row 0 cell space space 1 end cell cell space space 2 end cell end table close square brackets space space space space space space space space space space space space space space space space space space space equals space space space open square brackets table row cell 2 plus 4 plus 0 end cell cell space space space minus 2 plus 6 minus 4 end cell cell space space space 0 plus 8 minus 8 end cell row cell negative 4 plus 4 plus 0 end cell cell space space 4 plus 6 minus 4 end cell cell space space 0 plus 8 minus 8 end cell row cell 2 minus 2 plus 0 end cell cell space space space minus 2 minus 3 plus 5 space space end cell cell space space space space space 0 minus 4 plus 10 end cell end table close square brackets therefore space space space space BA equals space open square brackets table row cell 6 space end cell cell space space 0 end cell cell space space 0 end cell row 0 cell space space 6 end cell cell space space space 0 end cell row 0 cell space space 0 end cell cell space space 6 end cell end table close square brackets space space space space space... left parenthesis 2 right parenthesis From space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis space AB equals BA space space space space space space space space space space space space space space.... left parenthesis 3 right parenthesis Consider space the space equations space space straight x space – space straight y space equals 3 space space 2 straight x space plus space 3 straight y space plus space 4 straight z space equals space 17 space space straight y space plus space 2 space straight z space equals 7 space space These space equations space can space be space written space as open square brackets table row 1 cell negative 1 end cell cell space space 0 end cell row cell 2 space end cell cell space space space 3 end cell cell space space space 4 end cell row 0 cell space space 1 end cell cell space space 2 end cell end table close square brackets space space open square brackets table row straight x row straight y row straight z end table close square brackets space equals space open square brackets table row 3 row 17 row 7 end table close square brackets space Premutiplying space both space sides space by space open square brackets table row 2 cell space space space space space 2 end cell cell negative 4 end cell row cell negative 4 end cell cell space space space 2 end cell cell space space minus 4 end cell row 2 cell negative 1 end cell 5 end table close square brackets space space space we space get comma open square brackets table row 2 cell space space space space space 2 end cell cell negative 4 end cell row cell negative 4 end cell cell space space space 2 end cell cell space space minus 4 end cell row 2 cell negative 1 end cell 5 end table close square brackets space space open square brackets table row 1 cell negative 1 end cell cell space space 0 end cell row cell 2 space end cell cell space space space 3 end cell cell space space space 4 end cell row 0 cell space space 1 end cell cell space space 2 end cell end table close square brackets space space open square brackets table row straight x row straight y row straight z end table close square brackets space equals space open square brackets table row 2 cell space space space space space 2 end cell cell negative 4 end cell row cell negative 4 end cell cell space space space 2 end cell cell space space minus 4 end cell row 2 cell negative 1 end cell 5 end table close square brackets space space open square brackets table row 3 row 17 row 7 end table close square brackets or space space open square brackets table row 1 cell negative 1 end cell cell space space 0 end cell row cell 2 space end cell cell space space space 3 end cell cell space space space 4 end cell row 0 cell space space 1 end cell cell space space 2 end cell end table close square brackets space space open square brackets table row 2 cell space space space space space 2 end cell cell negative 4 end cell row cell negative 4 end cell cell space space space 2 end cell cell space space minus 4 end cell row 2 cell negative 1 end cell 5 end table close square brackets space space open square brackets table row straight x row straight y row straight z end table close square brackets space equals space space open square brackets table row cell 6 plus 34 minus 28 end cell row cell negative 12 plus 34 minus 28 end cell row cell 6 minus 17 plus 35 end cell end table close square brackets therefore space space open square brackets table row 6 0 0 row 0 cell space space space space space 6 space space space space end cell 0 row 0 0 6 end table close square brackets space space space open square brackets table row straight x row straight y row straight z end table close square brackets space space equals space open square brackets table row 12 row cell negative 26 end cell row 24 end table close square brackets therefore space space space open square brackets table row cell 6 straight x end cell row cell 6 straight y end cell row cell 6 straight z end cell end table close square brackets space equals space open square brackets table row 12 row cell negative 26 end cell row 24 end table close square brackets therefore space space 6 straight x equals 12 comma space 6 straight y equals negative 6 comma space 6 z equals 24 therefore space straight x equals 2 space comma space straight y equals negative 1.2 equals 4 space is space the space required space solution. space

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