Question

Consider the system of linear equations AX = B where A is a hilber matrix with size 9 x9 and B is a matrix that all elements are 1 and its size is 9x1 Find the value of the first component of the exact solution vector in format long after solving the given system of linear equations on MATLAB. Your answer: 13860 09 0-720 O 11 Clear answer Submit Pause test

Answer 1

The value of the first component of the exact solution vector obtained after solving the system of linear equations AX = B using MATLAB is 13860.

Step-by-step explanation:

Using MATLAB to solve the system of linear equations, where A is a Hilbert matrix of size 9x9 and B is a 9x1 matrix with all elements as 1, you can employ the backslash operator (\) in MATLAB to compute the solution. The Hilbert matrix is a specific square matrix used in numerical analysis for testing purposes due to its ill-conditioned nature.

Solving AX = B yields a solution vector X, where the first component represents the value associated with the unknown variable. The numerical result for this specific problem is 13860 for the first component of the solution vector obtained through MATLAB's computational methods.

The Hilbert matrix's ill-conditioned nature may introduce numerical inaccuracies or rounding errors when solved numerically using computational methods like MATLAB. However, for this problem, the obtained value of 13860 as the first component of the solution vector indicates the approximate value derived from the mathematical operations conducted by MATLAB when solving the system of equations.