The system of equations x + 2y + 3z = 4, 2x + 3y + 4z = 5,... | MATH - MINOR AND CO-FACTORS, PRODUCT OF DETERMINANTS | SolveeIt | Solveeit

Today, August 18

Question

The system of equations x + 2y + 3z = 4,

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

A

Infinitely many solution

B

No solution

C

Unique solution

D

None of these

Answer

Infinitely many solution

Explanation

Solution

Q D = $\left| \begin{matrix} 1 & 2 & 3 \\ 2 & 3 & 4 \\ 3 & 4 & 5 \end{matrix} \right|$ = 0

(Q entries in each row are in A.P. with common difference )

similarly D₁ = 0, D₂ = 0, D₃ = 0

\infinitely many solutions