Inverse

**christenc05** · November 23rd 2008, 03:48 PM

Set up a system belw as a matrix multiplication of the form AB=C. Find the inverse A^-1 of A and use it to solve the system.

3x + -6y + -17z = 288

11x + -17y + 110z = 79

-5x + 7y + 8z = 20.

I am able to get the first part of the matrix but I get lost when it comes to working on the second row.

**Moo** · November 24th 2008, 09:47 AM

Hello,

$\begin{pmatrix} 3&-6&-17 \\ 11&-17&110 \\ -5&7&8 \end{pmatrix} \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} 288 \\ 79 \\ 20 \end{pmatrix}$

This is your product.

After that, I don't know which methods you've used to calculate the inverse of a 3x3 matrix.
Here is the most common one :

Start with :
$\left( \begin{array}{ccc|ccc} 3&-6&-17&1&0&0 \\ 11&-17&110&0&1&0 \\ -5&7&8&0&0&1 \end{array} \right)$

And make row operations to find the ?'s in this matrix :
$\left( \begin{array}{ccc|ccc} 1&0&0&?&?&? \\ 0&1&0&?&?&? \\ 0&0&1&?&?&? \end{array} \right)$

The ?'s will form $A^{-1}$

After that, get back to the equation :
$AB=C$

multiply on the left by $A^{-1}$ :

$\underbrace{A^{-1}A}_{=I}B=A^{-1}C$

$B=\begin{pmatrix} x \\ y \\ z \end{pmatrix}=A^{-1}C=A^{-1}\begin{pmatrix} 288 \\ 79 \\ 20 \end{pmatrix}$

Thread: Inverse

LinkBack

Thread Tools

Display

Inverse

Similar Math Help Forum Discussions

left inverse equivalent to inverse

Inverse tan and inverse of tanh

secant inverse in terms of cosine inverse?

Prove that tan(2inverse tan) = 2tan(inverse tan + inverse tan x^3)

inverse trig values and finding inverse

Search Tags