Question

$If space open square brackets table row cell straight x minus straight y end cell cell space straight z end cell row cell 2 straight x minus straight y end cell cell space straight w end cell end table close square brackets space equals space open square brackets table row cell negative 1 end cell cell space 4 end cell row 0 cell space 5 end cell end table close square brackets comma space find space the space value space of space straight x plus straight y.$

Solution

Given space that space open square brackets table row cell straight x minus straight y end cell straight z row cell 2 straight x minus straight y end cell straight w end table close square brackets space equals space open square brackets table row cell negative 1 end cell cell space 4 end cell row cell space space 0 end cell cell space 5 end cell end table close square brackets

We need to find the value of x+y.

open square brackets table row cell straight x minus straight y end cell straight z row cell 2 straight x minus straight y end cell straight w end table close square brackets space equals space open square brackets table row cell negative 1 end cell cell space 4 end cell row cell space space 0 end cell 5 end table close square brackets

Two matrices A and B are equal to each other, if they have the same dimensions and the same elements

straight a subscript ij space equals space straight b subscript ij comma space space space for space straight i space equals space 1 comma 2 comma.... comma straight n and space straight j space equals space 1 comma space 2.... comma space straight m. rightwards double arrow space space space straight x minus straight y space equals negative 1 space.... left parenthesis 1 right parenthesis 2 straight x minus straight y equals 0..... left parenthesis 2 right parenthesis Equation space left parenthesis 2 right parenthesis minus left parenthesis 1 right parenthesis space is space straight x space equals space 1 Substituting space the space value space of space straight x space equals space 1 space in space equation space left parenthesis 1 right parenthesis comma space we space have 1 minus straight y space equals space minus 1 rightwards double arrow straight y space equals space 2 Therefore comma space straight x plus straight y space equals space 1 plus 2 space equals space 3

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