Subtract matrix from scalar Is this even possible? Since you can subtract on the right-hand side I think there must be a way to do it from left-hand side too.
I would like to calculate this:
3 - [2 1] = ??
 A: You can't actually add a scalar and a matrix.  In general, you can't add two matrices unless they are of the same dimension.  However, it is often the case that we denote a scalar matrix (a diagonal matrix all of whose entries are the same) by a scalar.  For example, you might write $4$ to denote the matrix $\begin{bmatrix}4 & 0 \\ 0 & 4\end{bmatrix}$.  The dimension of the matrix has to be understood from context.  This notation allows one to write, for example,
$$
4-\begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}=\begin{bmatrix}4 & 0 \\ 0 & 4\end{bmatrix}-\begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}=\begin{bmatrix}3 & -2 \\ -3 & 0\end{bmatrix}
$$
In your case, however, I have never seen a scalar used to denote a non-square matrix.
A: The previous answers that basically say "No, addition/subtraction is not defined between matrices of different dimensions" are the correct answer to your question.
Actually though, something like this is done formally in Clifford algebras. There are elements of the algebra identified with scalars, elements identified as vectors, (and even more elements with different identifications). Because they all live in an algebra, addition, subtraction and multiplication are defined between all of them.
However, this last item is probably not the answer you're looking for, because the addition is just formal: a scalar $\lambda$ plus a vector $v$ is just "$\lambda +v$", and there isn't a formula which presents it as another scalar, or another vector.
