How to augment a machine learning matrix?

[strat468]

TL;DR

augmenting a machine learning matrix

I have this equation which my professor has told me is correct so far.

$0 = -2*x^T(y-2(w*x+b))$

where
$x=\begin{bmatrix} 1 \\ 2 \end{bmatrix}$
$y = 6$
$w = \begin{bmatrix} w1 & w2 \end{bmatrix}$
$b = [b1]$

He told me to then augment w and b into one matrix in order to solve for both w and b.

How on earth do I do that?

 

[jedishrfu]

Start by computing $w \cdot x + b$ to get an expression in w1, w2 and b1 and go from there.

I'm assuming you meant to solve:

$0 = −2 \cdot x^T (y−2(w \cdot x+b)$

Also please use Latex to enter your expressions and show us your work. Our site uses Mathjax to render Latex and wew have a small guide to help you. See the link in my signature below.

 

[strat468]

Start by computing $w \cdot x + b$ to get an expression in w1, w2 and b1 and go from there.

I'm assuming you meant to solve:

$0 = −2 \cdot x^T (y−2(w \cdot x+b)$

Also please use Latex to enter your expressions and show us your work. Our site uses Mathjax to render Latex and we have a small guide to help you. See the link in my signature below.

Yes! Sorry Im new, I didnt know

 

[jedishrfu]

Not a problem did my suggestion help?

There's an online resource for Linear Algebra help at MathIsPower4u.com:

https://mathispower4u.com/linear-alg.php

that may be useful for future problems or to help in your understanding better.

 

[strat468]

Ill check out that resource.

Im not trying to be negative but Im reading that LaTeX guide, and Im putting delimiters in and its not doing anything

 

[strat468]

Ok got LaTeX working! Now I just need to figure out how to augment this

 

[jedishrfu]

The equation in your first post is somewhat confusing. $w \cdot x$ is a scalar and so wx+b is also a scalar leading to the conclusion that $0$ must be the zero row vector [0 0] ?

 

[strat468]

How is $w*x$ a scalar? x is a 2x1 matrix and w is a 1x2 matrix


I changed the formatting a bit so its easier to read

 

[strat468]

I see what youre implying. $w*x$ would be a scalar because it ends up being a 1x1 matrix. Youre correct.

All he told me was to set my equation to 0 and then solve for w and b. I then asked him how I solve for two unknown variables with only one equation and his reply was to augment w and b into one matrix.

 

[Mark44]

TL;DR Summary: augmenting a machine learning matrix

I have this equation which my professor has told me is correct so far.
$0 = -2*x^T(y-2(w*x+b))$

where
$x=\begin{bmatrix} 1 \\ 2 \end{bmatrix}$
$y = 6$
$w = \begin{bmatrix} w1 & w2 \end{bmatrix}$
$b = [b1]$

I'm a bit confused by this. x is defined as a 2 x 1 column vector. In the first equation, $x^T$ would therefore have to be a 1 x 2 row vector. Is this correct?

It would be useful to see the actual problem description as given by your professor.

 

[strat468]

I am currently on part 3
After pestering him over and over about this he finally gave me this....

But now the problem Im running into is

is a singular matrix making

impossible