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

$open square brackets table row cell straight x plus straight y plus straight z end cell row cell straight x plus straight z end cell row cell straight y plus straight z end cell end table close square brackets equals open square brackets table row 9 row 5 row 7 end table close square brackets$

Solution

We are given that
$open square brackets table row cell straight x plus straight y plus straight z end cell row cell straight x plus straight z end cell row cell straight y plus straight z end cell end table close square brackets equals open square brackets table row 9 row 5 row 7 end table close square brackets$

By definition of equality of matrices.
x.+ y + z = 9    ,..(1)
.x + z = 5    ...(2)
y + z = 7    ...(3)
Subtracting (2) from (1), y = 4
Subtracting (3) from (1). x = 2
∴from (2), 2 + z = 5 ;⇒ z =3
∴x = 2, .y = 4, z = 3

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