Not sure about this statement in vector space and matrix

[LCSphysicist]

Homework Statement

I will write in latex below

Relevant Equations

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Be $T_{1}, T_{2}$ upper and lower matrix, respectivelly. Show that we haven't matrix $M(NxN)$ such that $M(NxN) = T_{1}\bigoplus T_{2}$
I am not sure if i get what the statement is talking about, can't we call $T_{1},T_{2} = 0$? Where 0 is the matrix (NxN) with zeros on all its entries, in this way we can have M(NxN) as the sum of T1 and T2: T1=T2=M(NxN)

 

[fresh_42]

What is an upper matrix, or a lower matrix? I assume you forgot the word triangular? Which size do the $T_j$ have? And you cannot "set" the $T_j$, they are fixed, given.

It looks as if the key to the statement lies in the fact, that all matrices are required to be of the same size. You should also properly define what $T_1\oplus T_2$ means!