Question

Solve for.x and y, given that $open square brackets table row x y row cell 3 y end cell x end table close square brackets open square brackets table row 1 row 2 end table close square brackets equals open square brackets table row 3 row 5 end table close square brackets$

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Solution

open square brackets table row straight x straight y row cell 3 straight y end cell straight x end table close square brackets open square brackets table row 1 row 2 end table close square brackets equals open square brackets table row 3 row 5 end table close square brackets rightwards double arrow open square brackets table row cell straight x plus 2 straight y end cell row cell 2 straight x plus 3 straight y end cell end table close square brackets equals open square brackets table row 3 row 5 end table close square brackets By space definition space of space equality space of space matrices comma space space straight x space plus space 2 straight y space equals 3 space space space space space... left parenthesis 1 right parenthesis space space 2 straight x space plus space 3 straight y space equals space 5 space space space space... left parenthesis 2 right parenthesis space space Multiplying space left parenthesis 1 right parenthesis space and space 3 space and space left parenthesis 2 right parenthesis space by space 2 comma space we space get comma space 3 straight x space plus space 6 straight y space equals space 9 space space space space space space space... left parenthesis 3 right parenthesis space space 4 straight x space plus space 6 straight y space equals space 10 space space space space... left parenthesis 4 right parenthesis space space Subtracting space left parenthesis 3 right parenthesis space from space left parenthesis 4 right parenthesis comma space we space get comma space space straight x space equals space 1 therefore from space left parenthesis 1 right parenthesis comma space 1 space plus space 2 straight y space equals space 3 space rightwards double arrow space 2 straight y space equals space 2 space rightwards double arrow space straight y space equals space 1 space space therefore space we space have space space x space equals space 1 comma space straight y space equals space straight I.

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Matrices

Solve for.x and y, given that $open square brackets table row x y row cell 3 y end cell x end table close square brackets open square brackets table row 1 row 2 end table close square brackets equals open square brackets table row 3 row 5 end table close square brackets$

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