Science:Math Exam Resources/Courses/MATH307/April 2006/Question 01 (b)/Statement

Let PA = LU be

${\begin{bmatrix}1&0&0\\0&0&1\\0&1&0\end{bmatrix}}{\begin{bmatrix}1&0&2&3\\2&1&8&8\\0&1&4&2\end{bmatrix}}={\begin{bmatrix}1&0&0\\0&1&0\\2&1&1\end{bmatrix}}{\begin{bmatrix}1&0&2&3\\0&1&4&2\\0&0&0&0\end{bmatrix}}$

and

$b={\begin{bmatrix}b_{1}\\b_{2}\\b_{3}\end{bmatrix}}$

(b) Find the condition on b₁, b₂, and b₃ so that Ax = b has at least one solution.