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If Av = ), v for some veclor v. lhen A is an eigenvalue of

Elementary Linear Algebra: A Matrix Approach | 2nd Edition | ISBN: 9780131871410 | Authors: Lawrence E. Spence ISBN: 9780131871410 187

Solution for problem 41 Chapter 5.1

Elementary Linear Algebra: A Matrix Approach | 2nd Edition

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Elementary Linear Algebra: A Matrix Approach | 2nd Edition | ISBN: 9780131871410 | Authors: Lawrence E. Spence

Elementary Linear Algebra: A Matrix Approach | 2nd Edition

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Problem 41

If Av = ), v for some veclor v. lhen A is an eigenvalue of lhe matrix A

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Energy Behavior Temperature depends on amount of energy absorbed or reflected • Reflection depends on albedo – Describes the reflectivity of surfaces – Dark woodlands reflect 5 percent to 15 percent – Light grasslands reflect 25 percent • Absorption – Energy that is not reflected is absorbed – Different objects absorb different wavelengths – Hotter objects radiate energy more rapidly and at shorter wavelengths 9.3 Atmosphere Thin gaseous envelope that surrounds Earth – Gas molecules – Suspended particles of solid and liquid – Falling precipitation • Causes weather experienced every day • Responsible for trapping heat that keeps the Earth warm • Knowledge of structure and dynamics critical to understand severe weather Composition of the Atmosphere Composed mostly of nitrogen and oxygen – Smaller amounts of argon, water vapor, and carbon dioxide – Other trace elements and compounds • Water vapor – Important for cloud formation and circulation – Comes from evaporation off of Earth’s surface – Humidity describes amount of moisture in atmosphere at particular temperature • Relative humidity is the ratio of water vapor present to the amount that saturates the air • Increases at night because of cooler temps, decreases during the day due to heating Structure of the Atmosphere Water vapor content and temperature vary from Earth’s surface to it’s upper limits • Troposphere – All of Earth’s surface is within this layer – Upper boundary is tropopause – Temperature decreases with increasing altitude – Most visible characteristic is presence of clouds • Made from very small water droplets or ice crystals that condense from the atmosphere • Cumulus: puffy fair weather clouds • Cumulonimbus: tall, dark storm clouds – Contains most of the atmospheric carbon dioxide and methane Cloud Type Associated with Severe Weather Four aspects of atmosphere directly related to severe weather – Atmospheric pressure and circulation patterns – Vertical stability of the atmosphere – Coriolis effect (is a result of the earth's rotation. As air moves from high to low pressure in the northern hemisphere, it is deflected to the right by the Coriolis force.) – Interaction of different air masses Atmospheric Pressure and Circulation Atmospheric pressure also called barometric pressure – Weight of a column of air above a given point – Force exerted by molecules on surface • In the atmosphere, pressure decreases with increasing altitude – Nearly all of the weight of the atmosphere is in the lower atmosphere – Density and pressure decrease rapidly as you go to higher elevations Cont. Changes in air temperature and air movement are responsible for horizontal changes in pressure – Temperature influences pressure because cold air is more dense and exerts greater pressure on surface – Global variations in temperature cause global winds • At equator, air is warm and low in density – Creates low pressure zones at the equator – Air rises, condenses, forms clouds and rain – Cooler, drier air sinks at latitudes around 30° causing deserts – Similar vertical circulation cells observed at middle and high latitudes Cont. Jet streams – Midlatitude air masses of different temperatures colliding near tropopause • Westerly winds encircling the globe due to Coriolis effect • Greater the temperature difference, faster the flow Northern Hemisphere has two jet streams – Polar jet stream • Stronger of the two and boundary between cold arctic polar and warm subtropical and tropical air masses – Subtropical jet stream • Weak during the summer months but strongest in winter when temperature gradient between low­latitude and midlatitude air masses is greatest

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Chapter 5.1, Problem 41 is Solved
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Textbook: Elementary Linear Algebra: A Matrix Approach
Edition: 2
Author: Lawrence E. Spence
ISBN: 9780131871410

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If Av = ), v for some veclor v. lhen A is an eigenvalue of