how can I solve 14 equations with 14 unknowns?

Answer 1

Assume that your equations are in the form

a_1,1*x_1 + a_1,2*x_2 + ... + a_1,14*x_14 = c_1
a_2,1*x_1 + a_2,2*x_2 + ... + a_2,14*x_14 = c_2
.
.
.
a_14,1*x_1 + a_14,2*x_2 + ... + a_14,14*x_14 = c_14

Then we can form a matrix equation AX = C where the matrices are given by

A= [a_1,1 a_1,2 ............. a_1,14
a_2,1 a_2,2 .............. a_2,14
.
.
.
a_14,1 a_14,2 ............. a_14,14]

X = [x_1
x_2
.
.
.
x_14]

C = c_1
c_2
.
.
.
c_14]


Use a computer to compute the inverse of A (if A is not invertible, then you will not be able to solve the system). If we denote the inverse by A^-1, then we get AA^-1X = A^-1C ==> X = A^-1 C. The matrix X will be your solution.

Answer 2

With 14 groups of 14 unknown linear equations.

Answer 3

If you really have no idea how to approach this, you must start by solving one equation for one variable in terms of all the others and back-substitute until you come to one equation. It sounds more like an exercise to me. Any time you have the same number of knowns as unknowns, the set can be solved. Is this what you are asked to prove? With as many eq's as you have, if you really need actual solutions for all variables, it's going to take time.

Answer 4

You need to set up a matrix. Since you have 14 equations, you CAN solve this!

Answer 5

The way is very close to solving 3 eq with 3 unkowns. But it takes more time. If you want to do this things faster you should use an Engineering Calculator. It helps you a lot

Answer 6

once you've Ax = b, the position A is the coefficient matrix, x is the column vector of unknowns, and b is the column vector of constants, then purely write x = Ab on your case, A = [a million 2 -4 2 3 a million 4 7 lamda] b = [0 a million mu]' x is the three unknowns purely write x = Ab See the region lower than, for better examples

Answer 7

easy, break down the questions and simplify. solve one by one.....finding X is a challenge. Keep your formulas and factoring close by.....good luck...its easier than you think....

Answer 8

either solve it algebrically

or go on for matrix solution

sam ;)

Answer 9

you could probably use a comination of substitution and adding them together but i have never done that many before.

Answer 10

I'd use linear algebra (a martix)