The system of equations
$x + 2 y + 3 z = 4$
$2 x + 3 y + 4 z = 5$
$3 x + 4 y + 5 z = 6$ has

Many solutions

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

No solutions

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

Unique solution

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

None of these

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

Open in App

Solution

The correct option is D Many solutions
$⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 2 & 3 & 5 3 & 4 & 4 \end{matrix} ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ \begin{matrix} x y z \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 456 \end{matrix} ⎤ ⎥ ⎦ U s i n g r o w t r a n s f o r m a t i o n, R_{3} ⟶ R_{3} - (R_{1} + R_{2}) A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 2 & 3 & 4 0 & - 1 & - 2 \end{matrix} ⎤ ⎥ ⎦ R_{2} ⟶ R_{2} - 2 R_{1} A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 0 & - 1 & - 2 0 & - 1 & - 2 \end{matrix} ⎤ ⎥ ⎦ R_{3} ⟶ R_{3} - R_{2} A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 0 & - 1 & - 2 0 & 0 & 0 \end{matrix} ⎤ ⎥ ⎦ | A | = 0 \Rightarrow I n f i n i t e l y m a n y s o l u t i o n s e x i s t s$

Suggest Corrections

Similar questions

x + 2 y + 3 z = 4, 2 x + 3 y + 4 z = 5, 3 x + 4 y + 5 z = 6

The system of equations

X+2y+3z=4

2x+3y+4z=5

The system of equations

X+2y+3z=4

2x+3y+4z=5

2 x + 3 y + 4 z = 16

3 x + 2 y - 5 z = 8

5 x - 6 y + 3 z = 6

x + 2 y + 3 z = 14

2 x - y + 5 z = 15

3 x - 2 y - 4 z = - 13

Join BYJU'S Learning Program