1. ## Discriminant Rule Proof

My HW question is:

Show that...

is equal to...

My efforts:

Okay, so I started by expanding the first equation to this:

After combining terms, I got this:

Then, I multiplied the entire equation by :

From there, I've been unable to make any more forward progress. I'm pretty sure the first two terms can be rewritten like...

But I'm not sure about how the second two terms could be factorized. I can only assume that I've made an error in the expansion and simplification steps, but I've been unable the locate the error in my work (if one exists).

2. ## Re: Discriminant Rule Proof

When you expand the quadratic form, you cannot write something like .

Here are vectors, not a square matrix.

So you should get something like

3. ## Re: Discriminant Rule Proof

I've been able to reduce the initial expression to this, after following BGM's advice:

I am unsure of how to eliminate or combine the first two terms such that they are equal to the equation in the original post, though. Any suggestions would be welcome.

4. ## Re: Discriminant Rule Proof

The first two terms are equal,
because this quadratic term is just a real number (or a 1 by 1 matrix if you like)

So you can always take transpose on it.

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts