Consider the linear system ππ₯ = π, where π =Β \(\begin{bmatrix}2&-1\\\ -4&3\end{bmatrix}\)Β and b =Β \(\begin{bmatrix}-2\\\ 5\end{bmatrix}\).
Suppose π = πΏπ, where πΏ and U are lower triangular and upper triangular square matrices, respectively. Consider the following statements:
π: If each element of the main diagonal of πΏ is 1, then π‘ππππ(π) = 3.
π: For any choice of the initial vector π₯(0) , the Jacobi iterates π₯(π) , π = 1,2,3 … converge to the unique solution of the linear system ππ₯ = π.
ThenΒ
1
both π and π are TRUE
2
π is FALSE and π is TRUE
3
π is TRUE and π is FALSE
4
both π and π are FALSE