Jodi Arias -- Death Penalty Hangs in the Balance

Jodi Arias -- the woman found guilty of brutally murdering her ex-boyfriend Travis Alexander back in 2008 -- is back in court today in Arizona ... where a jury will decide whether to impose the death penalty.

Arias was convicted last week, and yesterday ... the jury decided she was eligible for the death penalty because of the extremely cruel nature of the murder.

Now, the same jury will decide if she'll actually get the death penalty ... or life in prison.

So far in court today, Travis' little brother and sister have given emotional statements in favor of giving Jodi the death sentence. Jodi was visibly upset the entire time.

Travis' little brother Steven told the jury, "I don't want these nightmares anymore. I don't want to have to see my brother's murderer anymore."

Travis' sister Samantha added, "Travis was our strength, our constant beacon of hope."

Officials say Alexander sustained nearly 30 stab wounds and a gunshot wound on June 4, 2008. Arias had argued she killed Alexander in self-defense.