For any rectangular matrix A, rref(A) gives the row reduced echelon matrix R. In matrix equation:

EA=R

My question is I know A, I know R, but there's seems no simple way to use this calculator to find E.

Please help.

Thanks.

Mike

You cannot divide matrices, but you can multiply by the inverse.

There's no inverses for rectangular matrices either. They are all "singular".

It is only possible for square matrices, because there could be multiple answers for a rectangular matrix.

No. For any (non zero) matrix A, its row reduced echelon form is unique and hence E is unique also.

There is a difference between reduced row echelon form and matrix multiplication.

Certainly there's a difference. A series of elementary row operations on A produces the row reduced echelon form R. These series of elementary row operations could be summarised by the elementary matrix E. Both R and E are unique, given any (non-zero) matrix A.

I think you have to apply the same row operations for reducing A to R to the identity matrix to get E. If find more information I will let you know. There aren't any built in commands to do this, but you may be able to adapt an existing program to do it.

Yes. I could do this by hand if the matrix A is small. It becomes impossible as A gets larger. The Nspire CX CAS has a rref(A) command to find R, so I suppose internally there is somewhere it stored E. I just wonder how to retrieve this.

Alternatively, perhaps someone good at linear algebra could give us a matrix formula to find E from A and R, so that we just have to punch in some operation sequence to find E. Personally, I don't understand why the calculator does not have a command to give E.

Oh, shouldn't that just be the right side of `rref(A|I)`? So

```
dim([A]
rref(augment([A],identity(Ans(1
```

and then strip off the first few columns somehow?

EDIT: Just noticed you were using the nSpire. So removing the left side should be easy.

You are a genius! This works but there are some problems:

1. dim(A) gives results like {2,3} and then the identity(Ans(1)) gives an error

2. I am not good at programming so I don't know how to automatically strip off the left few columns