Solve the equation for x, y, z and t, if

$2 space open square brackets table row x z row y t end table close square brackets plus 3 open square brackets table row 1 cell negative 1 end cell row 0 2 end table close square brackets equals 3 open square brackets table row 3 5 row 4 6 end table close square brackets$

Solution

The given matrix equation is

space space space space space space 2 space open square brackets table row straight x straight z row straight y straight t end table close square brackets plus 3 open square brackets table row 1 cell negative 1 end cell row 0 2 end table close square brackets equals 3 open square brackets table row 3 5 row 4 6 end table close square brackets or space space space space space space open square brackets table row cell 2 straight x end cell cell 2 straight z end cell row cell 2 straight y end cell cell 2 straight t end cell end table close square brackets plus open square brackets table row 3 cell negative 3 end cell row 0 6 end table close square brackets equals open square brackets table row 9 15 row 12 18 end table close square brackets or space space space space space space open square brackets table row cell 2 straight x end cell cell 2 straight z end cell row cell 2 straight y end cell cell 2 straight t end cell end table close square brackets equals open square brackets table row 9 15 row 12 18 end table close square brackets minus open square brackets table row 3 cell negative 3 end cell row 0 6 end table close square brackets or space space space space space space open square brackets table row cell 2 straight x end cell cell 2 straight z end cell row cell 2 straight y end cell cell 2 straight t end cell end table close square brackets equals open square brackets table row 6 18 row 12 12 end table close square brackets

By definition of equality of matrices, we get,
2x = 6, 2y= 12, 2z = 18,2 t = 12
∴x = 3, y = 6, z = 9, t = 6

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