Question

Let A be an m × n matrix and let 0 be the m × n matrix

that has all entries equal to zero. Show that A = 0 + A =

A + 0.

Short answer

A = 0 + A = A + 0

Step-by-step solution

Step 1:

A is a $m\times n$matrix and 0 is the $m\times n$matrix that has all entries equal to zero

we can rewrite the matrix A as $\left[a_{ij}\right]$where $a_{ij}$represents the elements in the i th row and j th column of A

the addition of two matrices adds the corresponding elements in the matrices

Adding 0 to a real number always results in the real number itself

$\begin{array}{r}0+A=\left[0\right]+\left[a_{ij}\right]\\ =a_{ij}\\ =A\\ A+0=\left[a_{ij}\right]+\left[0\right]\\ =a_{ij}\\ =A\end{array}$