Consider the following linear system.
$x + 2 y - 3 z = a$
$2 x + 3 y + 3 z = b$
$5 x + 9 y - 6 z = c$
The system is consistent if a,b and c safisfy the equation .

7 a - b - c = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3 a + b - c = 0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

3 a - b + c = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

7 a - b + c = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $3 a + b - c = 0$
$⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & - 3 2 & 3 & 3 5 & 9 & - 6 \end{matrix} ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ \begin{matrix} a b c \end{matrix} ⎤ ⎥ ⎦$ $\frac{R_{2} \to 2 R_{1} - R_{2}}{R_{3} \to 5 R_{1} - R_{3}}$
$⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & - 3 0 & 1 & - 9 0 & 1 & - 9 \end{matrix} ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ \begin{matrix} a 2 a - b 5 a - c \end{matrix} ⎤ ⎥ ⎦ \frac{(R_{3} \to R_{3} - R_{2})}{} ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 1 & 2 & - 3 & ⋮ & a 0 & 1 & - 9 & ⋮ & 2 a - b 0 & 0 & 0 & ⋮ & 3 a + b - c \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦$
For consistency $ρ (A) = ρ (A : B)$ ,which is possible only when
$3 a + b - c = 0$

Suggest Corrections

Similar questions

x + 2 y - 3 z = a

2 x + 6 y - 11 z = b

x - 2 y + 7 z = c

a, b

c

x - 2 y + 3 z = - 1

x - 3 y + 4 z = 1

- 2 x + 4 y - 6 z = k

x + y + 3 z = 4; 2 x + 2 y + 6 z = 7; 2 x + y + z = 10

2 x + p y + 6 z = 8

x + 2 y + q z = 5

x + y + 3 z = 4

p

q

Join BYJU'S Learning Program