My Math Forum Find A^-1 matrix

 Linear Algebra Linear Algebra Math Forum

September 22nd, 2018, 06:55 PM   #1
Senior Member

Joined: Apr 2017
From: New York

Posts: 162
Thanks: 6

Find A^-1 matrix

How can I do this ?
Attached Images
 CEA0156B-2431-47F9-814F-423E30FE10A6.jpg (8.0 KB, 8 views)

 September 22nd, 2018, 07:05 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,584 Thanks: 1430 $\begin{pmatrix} 1 &1 &1 &| &1 &0 &0\\ 0 &1 &1 &| &0 &1 &0\\ 0 &0 &1 &| &0 &0 &1 \end{pmatrix}$ $R1 \Rightarrow R1 - R2$ $\begin{pmatrix} 1 &0 &0 &| &1 &-1 &0\\ 0 &1 &1 &| &0 &1 &0\\ 0 &0 &1 &| &0 &0 &1 \end{pmatrix}$ $R2 \Rightarrow R2 - R3$ $\begin{pmatrix} 1 &0 &0 &| &1 &-1 &0\\ 0 &1 &0 &| &0 &1 &-1\\ 0 &0 &1 &| &0 &0 &1 \end{pmatrix}$ $A^{-1} =\begin{pmatrix} 1 &-1 &0\\ 0 &1 &-1\\ 0 &0 &1 \end{pmatrix}$ Thanks from v8archie and Leonardox
 September 22nd, 2018, 08:17 PM #3 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,690 Thanks: 2669 Math Focus: Mainly analysis and algebra On a $\LaTeX$ note, the array environment is your friend. $\left(\begin{array}{@{}ccc|ccc@{}} 1 &1 &1 &1 &0 &0\\ 0 &1 &1 &0 &1 &0\\ 0 &0 &1 &0 &0 &1 \end{array}\right)$ Thanks from Leonardox
 September 22nd, 2018, 08:35 PM #4 Senior Member   Joined: Sep 2016 From: USA Posts: 669 Thanks: 440 Math Focus: Dynamical systems, analytic function theory, numerics While technically Romsek's answer is correct, its a bit of overkill for a problem like this. You already have the matrix in upper triangular form which means it is trivial to solve $Ax = b$ for any $b$ you like. Choose $b$ to be a basis vector and back solve to determine each column of $A^{-1}$ instantly. In general, this works anytime you have already obtained an LU decomposition. In this case, the $L$ is just the identity matrix. Thanks from Leonardox
September 22nd, 2018, 08:46 PM   #5
Senior Member

Joined: Sep 2015
From: USA

Posts: 2,584
Thanks: 1430

Quote:
 Originally Posted by v8archie On a $\LaTeX$ note, the array environment is your friend. \begin{array}{@{}ccc|ccc@{}}

September 22nd, 2018, 08:55 PM   #6
Senior Member

Joined: Apr 2017
From: New York

Posts: 162
Thanks: 6

This is what I did to find A^-1
And then? Is that the answer of all question?
Attached Images
 C8044E60-CF1D-41D8-875F-C585AE274B1D.jpg (11.4 KB, 0 views)

 September 22nd, 2018, 08:58 PM #7 Senior Member   Joined: Apr 2017 From: New York Posts: 162 Thanks: 6 I guess Romsek found the A^-1 more practically then I did. so how should I continuity. I learned how to find inverse of any 3x3 matrix so far now.
 September 22nd, 2018, 09:13 PM #8 Senior Member   Joined: Apr 2017 From: New York Posts: 162 Thanks: 6 after finding A^-1 are we going to find x or b or both?
September 22nd, 2018, 09:19 PM   #9
Senior Member

Joined: Apr 2017
From: New York

Posts: 162
Thanks: 6

This is what I did. Did I continue correctly ?
Attached Images
 C06B6A99-E3CF-48B8-AE87-96AF91EDBE6E.jpg (5.4 KB, 1 views)

September 22nd, 2018, 09:21 PM   #10
Senior Member

Joined: Apr 2017
From: New York

Posts: 162
Thanks: 6

Oops sorry for the orientation. I corrected.
Attached Images
 480C65D0-4003-423C-94B4-3485AA7E6FC6.jpg (16.9 KB, 2 views)

 Tags find, matrix

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Leonardox Linear Algebra 2 September 22nd, 2018 08:39 PM imhotep Linear Algebra 4 February 15th, 2013 12:16 PM Nexusfactor Linear Algebra 1 February 6th, 2012 07:22 PM 450081592 Linear Algebra 1 November 15th, 2009 12:07 PM fakesmile Linear Algebra 1 July 12th, 2009 02:36 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top