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Find a different factorization of the A in Exercise 29, and thereby design a different ladder network whose transfer matrix is A.

$\left[\begin{array}{cc}1 & 0 \\ -1 / 6 & 1\end{array}\right]\left[\begin{array}{cc}1 & -6 \\ 0 & 1\end{array}\right]\left[\begin{array}{cc}1 & -6 \\ 0 & 1\end{array}\right]\left[\begin{array}{cc}1 & 0 \\ -1 / 36 & 0\end{array}\right]$

Algebra

Chapter 2

Matrix Algebra

Section 5

Matrix Factorizations

Introduction to Matrices

Missouri State University

Harvey Mudd College

Baylor University

Lectures

01:32

In mathematics, the absolu…

01:11

09:21

a. Compute the transfer ma…

14:22

Find a QR factorization of…

15:15

Exercises $22-26$ provide …

05:02

Use some form of technolog…

04:58

02:52

If a $3 \times 8$ matrix $…

03:57

05:41

02:36

Suppose $A_{11}$ is an inv…

03:34

If a $6 \times 3$ matrix $…

we were asked to find a different factories ation of the Given matrix from Exercise 29 and then design a different letter network with the transfer matrix of a so recall that from the previous problem transfer matrix A was four thirds negative. 12 negative 1/4 3 recall also from the previous exercise we had that when we constructed a circuit we had resistance are one of 36 owns distance are too of 12 homes and resistance R three of six homes and we saw that are one was a shunt circuit are two was a serious circuit and our three was a shunt circuit And so they had the factory ization 10 negative 1/6 0 one negative 12 01 times 10 negative 1/36 0. So now we can actually use this factory ization to find a new factory ization. So one of the easiest things to Dio is just simply break up this matrix in the middle by factoring into two different matrices. So this could be factored as 10 negative 16 zero one I mean, times matrix one negative 601 one Negative 601 You can just check this on your own. Recall that for unit upper and unit lower triangular matrices. They're multiplied by adding their non unit number if there are two by two together times 10 negative 1/36. So this is a new factory ization for a and we see that the network corresponding to this factor ization, has well looking on the right. This is a shunt circuit followed by to Siri's circuits, followed by a shunt circuit again with resistance is, uh, r one equals six are to equals. Sorry, Are one is 36 are two is six are three is six and our four is six.

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