$A=\begin{pmatrix} 2 & 5 & -3\\ 0 &-1 & 6 \end{pmatrix}$
$B=\begin{pmatrix} 3 & 1\\ 4 & -2\\ 0 & 6 \end{pmatrix}$, $A,B \in \mathbb{R}$
Is $A+B$ possible?
I have tried it on paper but I cannot decide how it could be done correctly : /
So now I'm wondering if this is possible defined at all?
By the way, would it be possible to do $A+1$ when $1 \in \mathbb{R}$
On
You're confusing things: $A,B$ are not $\in\Bbb{R}$. The numbers in $A,B$ are $\in \Bbb{R}$. The notation you are employing to say that those are real matrices does not exist in - at least - decent literature on the subject.
In the standard way the summation of matrices is defined ,which is based on sum of linear transformations, you can't sum that two matrices. Also, If $1$ is a number in $\Bbb{R}$, you can't sum it with a matrix unless you define it in some meaningful way.
I recommend you to review matrix operations. You can use anything on the internet, perhaps Khan academy. If you need a book, take Lang's: Introduction to Linear Algebra.
On
I think Ken Kuttler in his book A First Course in Linear Algebra (2014) puts it quite well. I'll refer to Definition 2.5 on page 61
Let $A = [a_{ij}]$ and $B = [b{ij} ]$ be two $m × n$ matrices. Then $A + B = C$ where $C$ is the $m × n$ matrix $C = [c_{ij} ]$ defined by $$c_{ij} = a_{ij} + b_{ij}$$
When rows and columns are of the same size, we are able to preform Matrix addtion. Eitherwise it is not possible.
No, it is not. The rule for matrix addition is element-wise. You can multiply them though!