TRUE OR FALSE (please answer all, will upvote immediately) 11. There are infinitely many values of the logarithm of a complex number z if you add 2m inits principal argument.12. Suppose the complex number z is situated along the real x axis, then the principalargument of z is equal to TT.13. Suppose the complex number is in polar form 2 < 450°, then principal argument of z isequal to 450°.14. Cofactor matrix is another matrix of order n in which all its elements in matrix A arereplaced by their respective signed minor.15. Suppose A is a square matrix with det(A)=0, then matrix A has an inverse matrix.

Answered: Image /qna-images/answer/20614a8f-2bc5-43e8-8fcd-c84c51cbf913.jpg

Answered: its principal argument. 12. Suppose the…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 5AEXP

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. Let $n \in \mathrm{N}^{*}$ and the equation:$$C_{2 n+1}^{1} x^{n}-C_{2 n+1}^{3} x^{n-1}+C_{2 n+1}^{5} x^{n-2}-\ldots+(-1)^{k} C_{2 n+1}^{2 k+1} x^{n-k}+\ldots+(-1)^{n} C_{2 n+1}^{2 n+1}=0$$Show that:a) the equation admits as roots the numbers::$\mathrm{x}_{\mathrm{k}}=\operatorname{ctg}^{2} \frac{k \pi}{2 n+1}$, for every $k \in\{1.2, \ldots . n\}$ b) $\frac{\pi^{2} n(2 n-1)}{3(2 n+1)^{2}}<\sum_{k=1}^{n} \frac{1}{k^{2}}<\frac{2 \pi^{2} n(n+1)}{3(2 n+1)^{2}}$ c) $\frac{\pi^{4} n(2 n-1)\left(4 n^{2}+10 n-9\right)}{45(2 n+1)^{4}}<\sum_{k=1}^{n} \frac{1}{k^{4}}<\frac{8 \pi^{4} n(n+1)\left(n^{2}+n+3\right)}{45(2 n+1)^{4}}$ d) $\lim _{n \rightarrow \infty} \sum_{k=1}^{n} \frac{1}{k^{2}}=\frac{\pi^{2}}{6}$ e) $\lim _{n \rightarrow \infty} \sum_{k=1}^{n} \frac{1}{k^{4}}=\frac{\pi^{4}}{4}$ Please check the attached picture for details. I need complete solution with explanation please. the all fifth subpoints are for the same problem and they are conected between them, but if…
13. The standard form of 3dy-xydx = 3y3e4x/3 by Bernoulli's equation is:
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