Mathematics, 08.12.2020 14:00 tassion3
find the spectral radius of A. Is this a convergent matrix? Justify your answer. Find the limit x=lim x^(k) of vector iteration
Answers: 3
![A = \left[\begin{array}{ccc} \frac{3}{4}& \frac{1}{4}& \frac{1}{2}\\ 0 & \frac{1}{2}& 0\\ -\frac{1}{4}& -\frac{1}{4} & 0\end{array}\right]](/tpl/images/0960/4917/757da.png)
![\left[\begin{array}{ccc} \frac{3}{4} - \lambda & \frac{1}{4}& \frac{1}{2}\\ 0 & \frac{1}{2} - \lambda & 0\\ -\frac{1}{4}& -\frac{1}{4} & 0 -\lambda \end{array}\right]=0 \\\\](/tpl/images/0960/4917/3c319.png)
![\to (\frac{3}{4} - \lambda ) [-\lambda (\frac{1}{2} - \lambda ) -0] - 0 - \frac{1}{4}[0- \frac{1}{2} (\frac{1}{2} - \lambda )] =0 \\\\\to (\frac{3}{4} - \lambda ) [(\frac{\lambda}{2} + \lambda^2 )] - \frac{1}{4}[\frac{\lambda}{2} - \frac{1}{4}] =0 \\\\\to (\frac{3}{8}\lambda + \frac{3}{4} \lambda^2 - \frac{\lambda^2}{2} - \lambda^3 - \frac{\lambda}{8} + \frac{1}{16}=0 \\\\\to (\lambda - \frac{1}{2}) (\lambda -\frac{1}{4}) (\lambda - \frac{1}{2}) =0\\\\](/tpl/images/0960/4917/2f8dc.png)
![\to c^{(k+1)} = A x^{k}+C \\\\\to x(0) = \left(\begin{array}{c}3&1&2\end{array}\right) , c = \left(\begin{array}{c}2&2&4\end{array}\right)\\\\ \to x^{(k+1)} = \left[\begin{array}{ccc} \frac{3}{4}& \frac{1}{4}& \frac{1}{2}\\ 0 & \frac{1}{2}& 0\\ -\frac{1}{4}& -\frac{1}{4} & 0\end{array}\right] x^k + \left[\begin{array}{c}2&2&4\end{array}\right] \\\\](/tpl/images/0960/4917/0aeac.png)
![\lim_{k \to \infty} x^k=o = \left[\begin{array}{c}0&0&0\end{array}\right]](/tpl/images/0960/4917/5fbf0.png)
Another question on Mathematics
Mathematics, 21.06.2019 15:30
What is the volume of a rectangular prism that is 120 centimeters by 2 meters by 1.5 meters in cubic meters?
Answers: 1
Mathematics, 21.06.2019 19:00
You give a $4 tip for a meal that cost $22. approximately what percent of the bill was your tip?
Answers: 1
Mathematics, 21.06.2019 20:10
Ascientist has discovered an organism that produces five offspring exactly one hour after its own birth, and then goes on to live for one week without producing any additional offspring. each replicated organism also replicates at the same rate. at hour one, there is one organism. at hour two, there are five more organisms. how many total organisms are there at hour seven? 2,801 19,531 19,607 97.655
Answers: 1
Mathematics, 22.06.2019 03:20
Arepresentative from plan 1 wants to use the graph below to sell health plans for his company. how might the graph be redrawn to emphasize the difference between the cost per doctor visit for each of the three plans? the scale on the y-axis could be changed to 0–100. the scale on the y-axis could be changed to 25–40. the interval of the y-axis could be changed to count by 5s. the interval of the y-axis could be changed to count by 20s.
Answers: 2
You know the right answer?
find the spectral radius of A. Is this a convergent matrix? Justify your answer. Find the limit x=li...
Questions
Computers and Technology, 20.11.2021 01:00
Mathematics, 20.11.2021 01:00
Chemistry, 20.11.2021 01:00
Chemistry, 20.11.2021 01:00
Mathematics, 20.11.2021 01:00
History, 20.11.2021 01:00
