$If space space straight A equals open square brackets table row cell 2 over 3 end cell 1 cell 5 over 3 end cell row cell 1 third end cell cell 2 over 3 end cell cell 4 over 3 end cell row cell 7 over 3 end cell 2 cell 2 over 3 end cell end table close square brackets space and space straight B space equals open square brackets table row cell 2 over 5 end cell cell 3 over 5 end cell 1 row cell 1 fifth end cell cell 2 over 5 end cell cell 4 over 5 end cell row cell 7 over 5 end cell cell 6 over 5 end cell cell 2 over 5 end cell end table close square brackets$ then computer 3A-5B

Solution

straight A equals open square brackets table row cell 2 over 3 end cell 1 cell 5 over 3 end cell row cell 1 third end cell cell 2 over 3 end cell cell 4 over 3 end cell row cell 7 over 3 end cell 2 cell 2 over 3 end cell end table close square brackets comma space space straight B space equals open square brackets table row cell 2 over 5 end cell cell 3 over 5 end cell 1 row cell 1 fifth end cell cell 2 over 5 end cell cell 4 over 5 end cell row cell 7 over 5 end cell cell 6 over 5 end cell cell 2 over 5 end cell end table close square brackets therefore space space 3 A minus 5 B equals 3 straight A equals open square brackets table row cell 2 over 3 end cell 1 cell 5 over 3 end cell row cell 1 third end cell cell 2 over 3 end cell cell 4 over 3 end cell row cell 7 over 3 end cell 2 cell 2 over 3 end cell end table close square brackets space minus 5 space open square brackets table row cell 2 over 5 end cell cell 3 over 5 end cell 1 row cell 1 fifth end cell cell 2 over 5 end cell cell 4 over 5 end cell row cell 7 over 5 end cell cell 6 over 5 end cell cell 2 over 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 space space space equals space open square brackets table row 2 3 5 row 1 2 4 row 7 6 2 end table close square brackets minus open square brackets table row 2 3 5 row 1 2 4 row 7 6 2 end table close square brackets space space space space space space space space space space 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 2 end cell cell 3 minus 3 end cell cell 5 minus 5 end cell row cell 1 minus 1 end cell cell 2 minus 2 end cell cell 4 minus 4 end cell row cell 7 minus 7 end cell cell 6 minus 6 end cell cell 2 minus 2 end cell end table close square brackets equals open square brackets table row 0 0 0 row 0 0 0 row 0 0 0 end table close square brackets equals 0

∴ 3A – 5B = O

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Matrices

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