Find the values of.x, y and z from the following equations :

$open square brackets table row cell straight x plus straight y end cell 2 row cell 5 plus straight z end cell cell straight x space straight y end cell end table close square brackets equals open square brackets table row 6 2 row 5 8 end table close square brackets$

Solution

We are given that
$open square brackets table row cell straight x plus straight y end cell 2 row cell 5 plus straight z end cell cell straight x space straight y end cell end table close square brackets equals open square brackets table row 6 2 row 5 8 end table close square brackets$

By definition of equality of matrices,
x+.y= 6    ....(1)
5 + z =5    ....(2)
x y =8    ...(3)
From (2). z= 0
From (I). y= 6 – x   ...(4)
Putting y = 6 –x in (3). we get.
x(6 – x) = 8 or 6 x – x² –8 = 0
∴x²–6x + 8 = 0 ⇒ (.x –2) (x–4) = 0;⇒ .x=2.4
;∴ from (4). y = 6 – 2. 6 – 4 = 4, 2
∴we have
x = 2, ,y = 4, z = 0 ; .x = 4, y = 2, z = 0

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