First slide

System of linear equations

Question

$T h e f o l l o w i n g s y s t e m o f l i n e a r e q u a t i o n s 2 x + 3 y + 2 z = 9, 3 x + 2 y + 2 z = 9, x - y + 4 z = 8$

Moderate

A

does not have any solution
B

Has infinitely many solutions
C

has a unique solution
D

has solution $(α, β, γ)$ such that $α^{2} + β^{2} + γ^{2} = 12$

Solution

$\begin{array}{l} The given system of equations is 2 x + 3 y + 2 z = 9, 3 x + 2 y + 2 z = 9, x - y + 4 z = 8 \\ The determinant of the coefficient matrix is D = |\begin{matrix} 2 & 3 & 2 \\ 3 & 2 & 2 \\ 1 & - 1 & 4 \end{matrix}| = 2 (10) - 3 (10) + 2 (- 5) = - 20 \neq 0 \end{array}$
$S i n c e t h e d e t e r m i n a n t o f t h e c o e f f i c i e n t m a t r i x i s n o n z e r o, t h e n o n - h o m o g e n e o u s s y s t e m o f e q u a t i o n s h a s a u n i q u e s o l u t i o n .$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App