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Home Question Bank Other Archive 2025 January 05

Other Questions from Jan 05,2025

Browse the Other Q&A Archive for Jan 05,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Given the matrix \( A=\left[\begin{array}{ccc}-2 & 7 & -1 \\ 0 & 3 & 0 \\ 0 & 0 & 4\end{array}\right] \). (a) Determine the eigenvalues of \( A \). (b) Using (a), find the determinant of \( A \). (c) Is \( A \) invertible? Why? (d) Deduce the eigenvalues of \( A^{-1} \). По заданной логической функции: 4. Построить карту Карно, упростить, сверить. Задания по вариантам: 8. \( f=\left(\overline{x_{1}} x_{2}+x_{1} \overline{x_{3}}\right)\left(x_{1} x_{2} x_{3}+\overline{x_{1} x_{2}}\right) \) The sets \( H \) and \( F \) are given below. \[ \begin{array}{l}H=\{-1,4,8\} \\ F=\{-2,-1,1,2,5,6\}\end{array} \] Find the intersection of \( H \) and \( F \). Find the union of \( H \) and \( F \). Write your answers using set notation (in roster form). \( H \cap F=\square \) The sets \( F \) and \( H \) are given below. \[ \begin{array}{l}F=\{c, f, h\} \\ H=\{b, e, f\} \\ F \cap H=\square\end{array} \] Find the union of \( F \) and \( H \). Find the intersection of \( F \) and \( H \). Write your answers using set notation (in roster form). \[ F H \] 2.5. consider the predicate \( p(x, y): y=x+3 \) what is the true values of the propositions \( p(1,2) \) and \( p(0,3) \) 2.6. State and explain Logic quantifiers 24. Given the propositional function, \( P(x): x+1>5 \), determine the values and the truth value for the following: a) \( P(8) \) b) \( P(2) \) c) \( P(8) \wedge[\sim P(2)] \) In a single integration DM scheme, the voice signal is sampled at a rate of 64 kHz . The maximum signal amplitude is 1 Volt. 1 . Determine the minimum value of step size to avoid slope overload. Determine granular noise power N0, if the voice signal bandwidth is 3.5 kHz . Assuming signal to be sinusoidal, calculate signal power So and signal to noise ratio (SNR).4. Assuming that the voice signal amplitude is uniformly distributed in the range, \( (-1,1) \), determine So and SNR. A binary receiver system receives a bit rate of 1 Mbps . The wave form amplitude is 5 mv and the noise power spectral density is 0.5 \( * 10^{\wedge}-11 \mathrm{~W} / \mathrm{Hz} \). Calculate the average bit error probability for BPSK Assume erfc \( (\mathrm{z})=\mathrm{e}^{\wedge}-\mathrm{z} 2 /[\operatorname{root}(\mathrm{pi})]^{*} \mathrm{z} \) 5. Reduce the matrix \( \left(\begin{array}{lll}1 & 5 & 7 \\ 0 & 4 & 3 \\ 0 & 0 & 1\end{array}\right) \) to Jordan Canonical form. Find the Rank of \( A=\left[\begin{array}{lll}1 & 2 & 3 \\ 2 & 3 & 4 \\ 0 & 2 & 2\end{array}\right] \)
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