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## Homework Statement

Let A,B be square matrices of order n. n>=2

lets A and B be matrices of Rank 1. What are the options of the Rank of A+B ?

## Homework Equations

## The Attempt at a Solution

I know that there are 3 possibilities, 2, 1 , 0. Just having trouble with coming up with a formula. i tried:

Rank(A+B) = dim(SP{Ac+Bc}) , (where Ac is the columns of A.)

I know also this equation

Rank of (A+B) = n - dim(P(A+B)) (where P denotes the solution space of (A+B)x = 0.