How i can the value for x y z by using a matrix

calculate the values of the (x,y, and z) for the following 3*3 linear algebraic equation . Where the inputs are 𝑎1−3, 𝑏1−3, 𝑐1−3, 𝑎𝑛𝑑 𝑞1−3 𝑎𝑠 𝑣𝑒𝑐𝑡𝑜𝑟𝑠. 𝑂𝑟𝑔𝑖𝑛𝑎𝑙 𝑓𝑜𝑟𝑚 𝑜𝑓 𝑒𝑞𝑎𝑡𝑖𝑜𝑛𝑠 ∶ 𝑎1𝑥 + 𝑏1𝑦 + 𝑐1𝑧 = 𝑞1 𝑎2𝑥 + 𝑏2𝑦 + 𝑐2𝑧 = 𝑞2 𝑎3𝑥 + 𝑏3𝑦 + 𝑐3𝑧 = 𝑞3 Try the code by entering different values of vectors.

[Dyuman Joshi]

How would you solve this on pen and paper utilizing concepts of Linear Algebra?

Answer 1

[Gayatri]

Hi Abdul,

To solve the given system of linear equations ∶ 𝑎1𝑥 + 𝑏1𝑦 + 𝑐1𝑧 = 𝑞1, 𝑎2𝑥 + 𝑏2𝑦 + 𝑐2𝑧 = 𝑞2 and 𝑎3𝑥 + 𝑏3𝑦 + 𝑐3𝑧 = 𝑞3​, use the ‘linsolve’ function.

function [x, y, z] = solveLinearEquations(a, b, c, q) 
    A = [a(1), b(1), c(1); a(2), b(2), c(2); a(3), b(3), c(3)]; 
    Q = [q(1); q(2); q(3)]; 
    solution = linsolve(A, Q); 
    x = solution(1); 
    y = solution(2); 
    z = solution(3); 
end 

Enter the different values for the coefficient vectors a, b, c and the constant vector q, then call the ‘solveLinearEquations’ function.

Please refer the below documentation for ‘linsolve’ function:

https://in.mathworks.com/help/matlab/ref/linsolve.html

I hope it helps!