find a basis M_23? what is the dimension of M_23? caracterized M_mn?

Question

this is a linear alebra problem

Answer 1

Do I understand that you want a basis of the space of all 2×3 matrices? Okay --

[1, 0, 0]
[0, 0, 0]

[0, 1, 0]
[0, 0, 0]

[0, 0, 1]
[0, 0, 0]

[0, 0, 0]
[1, 0, 0]

[0, 0, 0]
[0, 1, 0]

[0, 0, 0]
[0, 0, 1]

As you can see from the basis, the dimension of this space is 6.