Solve A in Ax = b

**goocreations** · June 26th 2011, 11:44 PM

If I have to vectors x and b, how can I solve matrix A in Ax = b? Or is this not possible?

Eg:

Code:

Ax = b
[a0, a1, a2, a3][x] = [x']
[b0, b1, b2, b3][y]   [y']

x, y, x' and y' are known. Is it possible to get a0-a3 and b0-b3?

Thanks

**Prove It** · June 27th 2011, 12:00 AM

$\displaystyle \begin{align*}\mathbf{Ax} &= \mathbf{b} \\ \mathbf{A}^T\mathbf{Ax} &= \mathbf{A}^T\mathbf{b} \\ (\mathbf{A}^T\mathbf{A})^{-1}\mathbf{A}^T\mathbf{Ax} &= (\mathbf{A}^T\mathbf{A})^{-1}\mathbf{A}^T\mathbf{b} \\ \mathbf{x}&= (\mathbf{A}^T\mathbf{A})^{-1}\mathbf{A}^T\mathbf{b}\end{align*}$

**goocreations** · June 27th 2011, 12:04 AM

Thank you. I'll try that.

**Prove It** · June 27th 2011, 12:09 AM

I have also realised that your matrix equation as written makes no sense, as the dimensions of the matrices $\displaystyle A$ and $\displaystyle x$ don't allow multiplication. Are you sure the equation wasn't

$\displaystyle \left[\begin{matrix}a_0 & b_0 \\ a_1 & b_1 \\ a_2 & b_2 \\ a_3 & b_3\end{matrix}\right]\left[\begin{matrix}x \\ y\end{matrix}\right] = \left[\begin{matrix}c_0 \\ c_1 \\ c_2\\ c_3\end{matrix}\right]$

because that WILL work...

**goocreations** · June 27th 2011, 12:12 AM

Thought I did something wrong. Thanks man

**goocreations** · June 27th 2011, 12:32 AM

I've now managed to compute x. Is there any way of getting A when I have x and b available?

**Prove It** · June 27th 2011, 01:19 AM

Use a similar method - postmultiply both sides by $\displaystyle \mathbf{x}^T$ in order to create a square matrix, then postmultiply both sides by $\displaystyle (\mathbf{xx}^T)^{-1}$ in order to get rid of the $\displaystyle x$ terms.

**goocreations** · June 27th 2011, 01:33 AM

Oh, that simple. Thank you very much

Thread: Solve A in Ax = b

LinkBack

Thread Tools

Display

Solve A in Ax = b

Re: Solve A in Ax = b

Re: Solve A in Ax = b

Re: Solve A in Ax = b

Re: Solve A in Ax = b

Re: Solve A in Ax = b

Re: Solve A in Ax = b

Re: Solve A in Ax = b

Similar Math Help Forum Discussions

need to solve summation equation to solve sum(x2)

How To Solve Integral of e? And solve velocity?

how do i solve this?

how to solve ..

please help me solve this

Search Tags