# LinearAlgebra.SingularException(2) when solving matrix equation which is solvable in Maple
**URL:** https://discourse.julialang.org/t/linearalgebra-singularexception-2-when-solving-matrix-equation-which-is-solvable-in-maple/62142
**Category:** General Usage
**Created:** [May 31, 2021, 3:54pm UTC](https://discourse.julialang.org/t/linearalgebra-singularexception-2-when-solving-matrix-equation-which-is-solvable-in-maple/62142 "2021-05-31T15:54:41Z")
**Posts on this page:** 8
**Page:** 1
### Author:  [@vikhes](https://discourse.julialang.org/u/vikhes)
#### Post date: [May 31, 2021, 3:54pm UTC](https://discourse.julialang.org/t/linearalgebra-singularexception-2-when-solving-matrix-equation-which-is-solvable-in-maple/62142/1 "2021-05-31T15:54:41Z")
Hi
I’m doing an assignment where I use my own implementation of Implicit Eulers with adaptive step size using error estimation. For this, I have made my own implementation of the Newton solver. In one ODE system, my numerical solver fails to solve the following matrix equation.
```julia
dRdt = [2.7347115660463565e46 1.4462465159832052e46 7.06637105328182e46; 5.469423132092713e46 2.8924930319664105e46 1.413274210656364e47; -3.658477011433253e48 -1.9347779478036194e48 -9.453339201714811e48]
R = [1.0026696232160644e47, 2.0053392464321287e47, -1.3413640444362068e49]
dRdt\R
```
This returns the error
ERROR: LoadError: LinearAlgebra.SingularException(2)
I have tried to solve the equation in Maple and it solves it without an issue (see image below)
Does anyone know what is wrong?
---
### Author:  [@dmbates](https://discourse.julialang.org/u/dmbates)
#### Post date: [May 31, 2021, 4:03pm UTC](https://discourse.julialang.org/t/linearalgebra-singularexception-2-when-solving-matrix-equation-which-is-solvable-in-maple/62142/2 "2021-05-31T16:03:02Z")
> [@vikhes](#):
>
> ```julia
> dRdt = [2.7347115660463565e46 1.4462465159832052e46 7.06637105328182e46; 5.469423132092713e46 2.8924930319664105e46 1.413274210656364e47; -3.658477011433253e48 -1.9347779478036194e48 -9.453339201714811e48]
> R = [1.0026696232160644e47, 2.0053392464321287e47, -1.3413640444362068e49]
>
> dRdt\R
>
> ```
>
> This returns the error
>
> ERROR: LoadError: LinearAlgebra.SingularException(2)
>
> I have tried to solve the equation in Maple and it solves it without an issue (see image below)
> 
>
> Does anyone know what is wrong?
The system is ill-conditioned
```julia
julia> dRdt = [2.7347115660463565e46 1.4462465159832052e46 7.06637105328182e46
5.469423132092713e46 2.8924930319664105e46 1.413274210656364e47
-3.658477011433253e48 -1.9347779478036194e48 -9.453339201714811e48];
julia> cond(dRdt)
2.885773849638737e32
```
---
### Author:  [@cvanaret](https://discourse.julialang.org/u/cvanaret)
#### Post date: [May 31, 2021, 5:07pm UTC](https://discourse.julialang.org/t/linearalgebra-singularexception-2-when-solving-matrix-equation-which-is-solvable-in-maple/62142/3 "2021-05-31T17:07:35Z")
I would factor out 10^{46} from the system 😉
---
### Author:  [@dmbates](https://discourse.julialang.org/u/dmbates)
#### Post date: [May 31, 2021, 5:11pm UTC](https://discourse.julialang.org/t/linearalgebra-singularexception-2-when-solving-matrix-equation-which-is-solvable-in-maple/62142/4 "2021-05-31T17:11:24Z")
I don’t think that will affect the condition number, will it?
```julia
julia> svdvals(dRdt)
3-element Vector{Float64}:
1.0321007400020088e49
1.432533639792516e33
3.576512900105512e16
julia> svdvals(dRdt .* 1.0e-46)
3-element Vector{Float64}:
1032.1007400020085
1.2316027007572554e-13
2.9065558295847953e-16
```
---
### Author:  [@dmbates](https://discourse.julialang.org/u/dmbates)
#### Post date: [May 31, 2021, 5:15pm UTC](https://discourse.julialang.org/t/linearalgebra-singularexception-2-when-solving-matrix-equation-which-is-solvable-in-maple/62142/5 "2021-05-31T17:15:29Z")
I guess I should have looked at the results before I said that it wouldn’t affect the condition number. The condition number for the scaled matrix is on the order of 10^19 instead of 10^33 but it is still computationally singular.
---
### Author:  [@ctkelley](https://discourse.julialang.org/u/ctkelley)
#### Post date: [May 31, 2021, 5:23pm UTC](https://discourse.julialang.org/t/linearalgebra-singularexception-2-when-solving-matrix-equation-which-is-solvable-in-maple/62142/7 "2021-05-31T17:23:28Z")
The condition number won’t change in infinite precision, but that’s not what we’re dealing with here. Anyhow, as @dmbates observes, 10^19 is still bad enough to make most solvers complain.
---
### Author:  [@cvanaret](https://discourse.julialang.org/u/cvanaret)
#### Post date: [May 31, 2021, 5:27pm UTC](https://discourse.julialang.org/t/linearalgebra-singularexception-2-when-solving-matrix-equation-which-is-solvable-in-maple/62142/8 "2021-05-31T17:27:28Z")
Indeed, my bad. You probably only gain floating-point representation space.
My guess is that Maple computes the solution analytically (relatively easy for 3x3).
---
### Author:  [@vikhes](https://discourse.julialang.org/u/vikhes)
#### Post date: [June 3, 2021, 7:24am UTC](https://discourse.julialang.org/t/linearalgebra-singularexception-2-when-solving-matrix-equation-which-is-solvable-in-maple/62142/9 "2021-06-03T07:24:23Z")
Thank you all for your answers they were very helpful to understand what was going on! I ended up tweaking the tolerances of my solver, which avoided that ill-conditioned system and solved the ODEs.