Let A be as above, consider Ax = b where b = (31, 2, 21, 11). Find x1 using Cramer’s rule. (You may use MATLAB/Octave to compute the determinants, but write out what you are computing.).Matrix a= 8 6 -3 204 2 -5 -78 2 7 204 2 -11 -4
Accepted Solution
A:
Answer:[tex]x_1=1[/tex]Step-by-step explanation:The matrix of the system of equations is [tex]A=\left[\begin{array}{cccc}8&6&-3&20\\4&2&-5&-7\\8&2&7&20\\4&2&-11&-4\end{array}\right][/tex].Remember that using Cramer's Rule [tex]x_1=\frac{det(A_1)}{det(A)}[/tex], where [tex]A_1[/tex] is the same matrix A change the first column of A by b. Then [tex]A_1=\left[\begin{array}{cccc}31&6&-3&20\\2&2&-5&-7\\21&2&7&20\\11&2&-11&-4\end{array}\right][/tex].Using Octave we calculate the determinants and obtain that det(A)=-3840 and [tex]det(A_1)=-3840[/tex].Then [tex]x_1=\frac{-3840}{-3840}=1[/tex]