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## Homework Statement

Let A be the following 2x2 matrix:

s 2s

0 t

Find a subspace B of M

_{2x2}where M

_{2x2}= A (+) B

## Homework Equations

A ∩ B = {0}

if u and v are in M

_{2x2}, then u + v is in M

_{2x2}

if u is in M

_{2x2}, then cu is in M

_{2x2}

## The Attempt at a Solution

Let B be the following 2x2 matrix:

0 0

r 0

Because they are both subspace, they intersect at the zero vector and thus the set {0}, the zero subspace, is a subspace of M

_{2x2}. We then have

M

_{2x2}= A (+) B:

M

_{2x2}= A + B /\ A ∩ B = {0}