Hi so I have a problem where I need to solve x4 simultaneous equations using matrices and have no idea how to even formulate the simultaneous equations correctly. I have attached a copy of the question.
First Write down the equations for each temperature. Put the unknowns temperatures on one side and the values on the other. For example, if I'm reading the problem correctly, T
1 is the average of the 4 temperatures of the one above (40), the one to the right (T
2), the one below(T
3) and the one to the left (0) so we write
\(\displaystyle T_1\, =\, \frac{40\, +\, T_2\, +\, T_3\, +\, 0}{4}\)
Bringing all the T's to the left side and leaving the numbers on the right hand side gives
4 T
1 + (-1) T
2 + (-1) T
3 + 0 T
4 = 40
gives a first row for the matrix of (4, -1, -1, 0). You could also have written that as
(1) T
1 + (-1/4) T
2 + (-1/4) T
3 + 0 T
4 = 10
to get an equivalent row with a different B
1
