This answer deserves to be on top. Really great answer, made me realize that linear congruences and diophantine equations are inter-convertible.

Remember that augmented matrices correspond to systems of linear equations. Once you've finished row-reducing, turn the row-reduced matrix back into a system of equations and solve for the …

The SVD Solution to Linear Least Squares / Linear System of Equations Ask Question Asked 9 years, 6 months ago Modified 1 month ago

Jan 24, 2015 · 2 If I have 4 equations and 3 unknowns, I could solve for the 3 unknowns using the first 3. How does it ensure that the 4th equation is also satisfied? In this case, what should be the usual …

1 Well, in this answer I will use matrices to solve the problem. For that, I will transform the given equations to a matrix equation.

Jun 11, 2017 · Using your second last equation, we get $1=3-2$. Both $2$ and $3$ are remainders in other equations, so you can replace them by $20-3\cdot6$ and $23-20$, respectively. Keep …

Feb 24, 2015 · Using LU Decomposition how can I solve for vector $x$ in the system $Ax = b$, given $A$ and $b$. For simplicities sake where $A$ is a 3x3 matrix and $b$ is a vector of size 3.

Jun 16, 2018 · Explore related questions linear-algebra systems-of-equations numerical-linear-algebra See similar questions with these tags.

Feb 1, 2017 · 2 This question already has answers here: Solve a linear system with more variables than equations (2 answers)

Sep 20, 2016 · 1) A system of linear equations has either no solution, a unique solution, or infinitely many solutions. 2) For square matrix $A$, $det (A) \ne 0$ iff the system has a unique solution.