Numerade

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(2.4) Let V and W be vector spaces, and let T: V \rightarrow W be linear and invertible. Prove that $T^{-1}$: W \rightarrow V is linear. (2.5) Let B be a fixed n x n invertible matrix, and F a field. Define $\Phi_B$: $M_{n \times n}(F)$ \rightarrow $M_{n \times n}(F)$ by $\Phi_B(A) = B^{-1}AB$. Prove that $\Phi_B$ is an isomorphism. (2.6) Suppose that V is a vector space with ordered basis $\beta$. Suppose that T: V \rightarrow V is linear and that $[T]_\beta = \begin{pmatrix} 2 & 1\\ 1 & 1 \end{pmatrix}$. (a) Show that T is invertible. (b) Determine $[T^{-1}]_\beta$ and explain your reasoning.

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The term ____________________ describes a sleep disorder consisting of recurring episodes of falling asleep during the day.

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C(s) = \frac{1}{2s+1} \frac{x}{s^2} C(s) = \frac{1}{(2s+1)s^2} C(s) = \frac{A}{s} + \frac{B}{s^2} + \frac{C}{2s+1} (C(s) = \frac{As^2 + Bs + C}{s^3} \frac{C}{2s+1} = t - t + t

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A 25 foot ladder leans against a building so that the angle between the ground and the ladder is 80°. How high does the ladder reach up the side of the building? Round to 2 decimal places.

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Accurately sketch the following signal from $t = -6$ to $t = 6$. Label all axes. $x(t) = \text{rect}\left(\frac{t}{4}\right) * (\delta(t + 3) + \delta(t) + \delta(t - 3))$

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(1 point) In cases where the confidence level leads to an area underneath the probability density function for either the standard normal or the t distribution that is not exactly listed on the tables, linear interpolation is used. We have seen a little bit of this in the $z_\alpha$ for the 90% and 99% confidence levels. At 99% confidence, the significance level, $\alpha$, is 0.01 and the area underneath the standard normal pdf to the left of $z_\alpha$ is 0.995. The area 0.995 is halfway in between 0.9949 and 0.9951 on the z-table, therefore $z_\alpha$ is 2.575, the value halfway between 2.57 and 2.58. Similarly, at 91% confidence, the area underneath the standard normal pdf to the left of $z_\alpha$ is 0.955. The value, 0.955, is about 0.555555 of the distance between 0.9545 and 0.9554, the two closest values found on the z-table, and therefore $z_\alpha$ should be the value about 0.555555 of the distance between 1.69 and 1.70, or 1.695555. Try this out on the following problem. A medical statistician wants to estimate the average weight loss of people who are on a new diet plan. Assume that the standard deviation of the population of weight loss is about 2.5 pounds. In a sample of 17 subjects on the new diet plan, the average average weight loss was 11.5 pounds. What is the 96% confidence interval estimate for the average weight loss for anyone that follows the new diet plan? $\leq \mu \leq$

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The frequency distribution displayed below presents the variable likeability of recommendation based on the question "How likely is it that you would recommend our hotel to a friend or colleague?". Please calculate the median and type in the correct answer (in numbers). Value label Value Frequency (N) % Valid % Cumulative % very unlikely 1 1 5,3 0,5 0,5 2 0 0,0 0,0 0,5 3 0 0,0 0,0 0,5 4 2 10,5 0,9 1,4 5 3 15,8 1,4 2,8 6 4 21,1 1,8 4,6 very likely 7 6 31,6 2,8 7,3 Missing 3 15,8 Total 19 100 7,3 Answer:

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Adjusting entries are made to ensure that: Expenses are recognized in the period in which they are incurred Revenues are recorded in the period on which they are earned Balance sheet and income statement accounts have correct balances at the end of the accounting period All of the above Only a and b

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Refer to the figure at right. The slope of the budget line equals A. -1.5. B. -1. C. -0.5. D. -2.

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5 ft < Problem 3/10 > D B C P Q 10 ft 10 ft Using the method of joints, determine the force in each member of the truss shown. The load P = Q = 14 kips. Round the final answers to their nearest kip. Use positive values for tension and negative for compression. FDA = FDC = FCA = FCB = FBA =

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sharon d.