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[SOLVED] -311.2.2.31 inverse matrix

karush

Well-known member
Jan 31, 2012
3,068
$\tiny{311.2.2.31}$
$A=\left[\begin{array}{rrrrr}
1&0&-2\\-3&1&4\\2&-3&4
\end{array}\right]$
RREF with augmented matrix
$\left[ \begin{array}{ccc|ccc}
1&0&-2&1&0&0 \\&&&\\-3&1&4&0&1&0 \\&&&\\ 2&-3&4&0&0&1\end{array}\right]
\sim
\left[ \begin{array}{ccc|ccc}1&0&0&8&3&1 \\&&&\\0&1&0&10&4&1 \\&&&\\ 0&0&1&\dfrac{7}{2}&\dfrac{3}{2}&\dfrac{1}{2}
\end{array}\right]
\quad \therefore A^{-1}=\left[
\begin{array}{ccc}8 & 3 & 1 \\\\ 10 & 4 & 1 \\\\ \dfrac{7}{2} & \dfrac{3}{2} & \dfrac{1}{2} \end{array} \right]$

ok I left out the row reduction steps
but I tried to use the desmos matrix calculator to check this
but after you put in the matrix didn't see how to run it.
 

topsquark

Well-known member
MHB Math Helper
Aug 30, 2012
1,274
This is why I prefer W|A.

-Dan
 

karush

Well-known member
Jan 31, 2012
3,068
when all else fails there is W|A
 

Country Boy

Well-known member
MHB Math Helper
Jan 30, 2018
821
Do you really have to use some kind of calculator do the arithmetic for you?

Surely it is not that hard to do
$\begin{bmatrix}1 & 0 & -2 \\ -3 & 1 & 4 \\2 & 3 & 4 \end{bmatrix}\begin{bmatrix}8 & 3 & 1 \\ 10 & 4 6 & 1 \\ \frac{7}{2} & \frac{3}{2} & \frac{1}{2}\end{bmatrix}= \begin{bmatrix}8- 7 & 3- 3 & 1- 1\\ -24+ 10+ 14 & -9+ 4+ 6 & -3+ 1+ 2 \\ 16- 30+ 14 & 6- 12+ 6 & 2- 3+ 2 \end{bmatrix}= \begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$
and
$\begin{bmatrix}8 & 3 & 1 \\ 10 & 4 6 & 1 \\ \frac{7}{2} & \frac{3}{2} & \frac{1}{2}\end{bmatrix}$$\begin{bmatrix}8 & 3 & 1 \\ 10 & 4 6 & 1 \\ \frac{7}{2} & \frac{3}{2} & \frac{1}{2}\end{bmatrix}$$= \begin{bmatrix}8- 9+ 2 & 3- 3 & -16+ 12+ 4 \\ 10- 12+ 2 & 4- 3 & -20+ 16+ 4 \\ \frac{7}{2}- \frac{9}{2}+ 1 & \frac{3}{2}- \frac{3}{2} & -7+ 6+ 2 \end{bmatrix}=$$ \begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$.

(I'm just too old!)
 

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
1,007
Any operation with matrices larger than 2 by 2 isn't meant to be done by hand, especially if one is prone to arithmetic errors. ;)
 

karush

Well-known member
Jan 31, 2012
3,068
its kinda like a bingo game