Question: Prove that diagonally dominated matrices are always invertible. Now, what is a diagonally dominated matrix? It is a square matrix that has each of

Prove that diagonally dominated matrices are always invertible. Now, what is a

Prove that diagonally dominated matrices are always invertible. Now, what is a diagonally dominated matrix? It is a square matrix that has each of it's diagonal values larger in magnitude than all the other values in the rows combined. (Bonus) To be mathematically precise, for every diagonal value a,,i, |ai,i| > Eit; lai,jl .(1) |ai,i| > lai,1[+ |lai,2| + .. + lai,i-1|+ lai,i+1|+ ... + lai,n| For example, 3 1 1 5 2 2 6 1 3 1 -3 1 1 3 1 1 4

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