Question

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 20

4 2 -5 -7

8 2 7 20

4 2 -11 -4

Answer 1

Answer:

$x_1=1$

Step-by-step explanation:

The matrix of the system of equations is $A=\left[\begin{array}{cccc}8&6&-3&20\\4&2&-5&-7\\8&2&7&20\\4&2&-11&-4\end{array}\right]$.

Remember that using Cramer's Rule $x_1=\frac{det(A_1)}{det(A)}$, where $A_1$ is the same matrix A change the first column of A by b. Then $A_1=\left[\begin{array}{cccc}31&6&-3&20\\2&2&-5&-7\\21&2&7&20\\11&2&-11&-4\end{array}\right]$.

Using Octave we calculate the determinants and obtain that det(A)=-3840 and  $det(A_1)=-3840$.

Then $x_1=\frac{-3840}{-3840}=1$