Q5Single correct4 Marks26 Oct 2025

Consider the system of linear equations with unknowns $x,y,z$ given by $$\begin{bmatrix}1&2&1\\3&0&-1\\1&8&5\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}b_1\\b_2\\b_3\end{bmatrix},$$ where $b_1,b_2,b_3\in\mathbb{R}$. Choose the equation to be satisfied by $b_1,b_2,b_3$ to ensure that the given system of equations has a solution.

A

$2b_1+b_2-b_3=0$

B

$2b_1-b_2+b_3=0$

C

$-4b_1+b_2-b_3=0$

D

$-4b_1+b_2+b_3=0$