tag:blogger.com,1999:blog-9004452969563620551.post404655538761552101..comments2019-08-19T10:06:27.486+05:30Comments on Paramanand's Math Notes: Matrix Inversion: Partition MethodUnknownnoreply@blogger.comBlogger3125tag:blogger.com,1999:blog-9004452969563620551.post-77886129938091161902013-04-10T03:10:26.966+05:302013-04-10T03:10:26.966+05:30Really helpful. Thanks for sharing sirji :)Really helpful.<br />Thanks for sharing sirji :)Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-9004452969563620551.post-53921623302495840582013-03-10T11:01:00.006+05:302013-03-10T11:01:00.006+05:30There&#39;s another description here (using differ...There&#39;s another description here (using different symbols):<br />Partition method (Escalator Method) of finding the inverse of a Matrix <br />http://mathumatiks.com/index.php?module=subpage&amp;nid=268Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-9004452969563620551.post-39702440189888291042013-02-15T14:18:19.995+05:302013-02-15T14:18:19.995+05:30From Karan (comment on http://paramanands.wordpres...From Karan (comment on http://paramanands.wordpress.com/2012/08/19/matrix-inversion-partition-method/):<br />------------<br /><br />Sir, I would really appreciate your demonstrating the solution of a 5*5 matrix by this method. Are we supposed to use the inverse of the 3*3 matrix to find inverse of the 4*4 matrix which could be further used for finding the inverse of 5*5 matrix? How is that done? When we put the matrix &#39;X&#39; so as to find inv(5*5), we&#39;re required to calculate the inverse of &#39;X&#39;, right?<br /><br />My Reply:<br />---------<br /><br />Hello Karan,<br />If you observe the example carefully you will see that we have started with the inverse of 2x2 matrix and then using this found inverse of 3x3 matrix. Now repeating the same procedure we can find inverse of 4x4 matrix using the already obtained inverse of 3x3 matrix. Repeating further we can get the inverse of 5x5 matrix.<br /><br />I can not provide all the calculations, as it will be lengthy but I will provide a sample example:<br /><br />Let $\displaystyle A_{5} = \begin{bmatrix} a &amp; b &amp; c &amp; d &amp; e\\<br />f &amp; g &amp; h &amp; i &amp; j\\<br />k &amp; l &amp; m &amp; n &amp; o\\<br />p &amp; q &amp; r &amp; s &amp; t\\<br />u &amp; v &amp; w &amp; x &amp; y\end{bmatrix}$<br /><br />Then we first find the inverse of<br />$\displaystyle A_{2} = \begin{bmatrix} a &amp; b \\ f &amp; g\end{bmatrix}$<br />Next we find inverse of<br />$\displaystyle A_{3} = \begin{bmatrix} a &amp; b &amp; c \\ f &amp; g &amp; h \\ k &amp; l &amp; m \end{bmatrix}$<br />Then we find inverse of<br />$\displaystyle A_{4} = \begin{bmatrix} a &amp; b &amp; c &amp; d\\ f &amp; g &amp; h &amp; i \\ k &amp; l &amp; m &amp; n \\ p &amp; q &amp; r &amp; s\end{bmatrix}$<br />and then finally the inverse of $A_{5}$.<br /><br />In each step the inverse calculated from previous step is used.paramanandhttps://www.blogger.com/profile/03855838138519730072noreply@blogger.com