Examine the consistency of the system of equations $x + y + z = 1$ , $2 x + 3 y + 2 z = 2$ , $a x + a y + 2 a z = 4$

Open in App

Solution

Given system of equations
$x + y + z = 1$
$2 x + 3 y + 2 z = 2$
$a x + a y + 2 a z = 4$
This can be written as
$A X = B$
where $A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 1 & 1 2 & 3 & 2 a & a & 2 a \end{matrix} ⎤ ⎥ ⎦, X = ⎡ ⎢ ⎣ \begin{matrix} x y z \end{matrix} ⎤ ⎥ ⎦, B = ⎡ ⎢ ⎣ \begin{matrix} 124 \end{matrix} ⎤ ⎥ ⎦$

Here, $| A | = 1 (6 a - 2 a) - 1 (4 a - 2 a) + 1 (2 a - 3 a)$
$\Rightarrow | A | = a \neq 0$
Since, $| A | \neq 0$
Hence, the system of equations is consistent.

Suggest Corrections

Similar questions

Examine the consistency of the system of equations.

x + y + z = 1

2x + 3y + 2z = 2

ax + ay + 2az = 4

3 x - y - 2 z = 2, 2 y - z = - 1, 3 x - 5 y = 3

x + y - 2 z = 0

2 x - 3 y + z = 0

x - 5 y + 4 z = k

x + y + z = 2

2 x + 3 y + 2 z = 5

2 x + 3 y + (a^{2} - 1) z = a + 1

Join BYJU'S Learning Program