Intermediate Algebra
10th Edition
ISBN: 9781305191495
Author: Jerome E. Kaufmann; Karen L. Schwitters
Publisher: Cengage Learning US
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Chapter 11.5, Problem 47PS
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You are given a plane Π in R3 defined by two vectors, p1 and p2, and a subspace W in R3 spanned by twovectors, w1 and w2. Your task is to project the plane Π onto the subspace W.First, answer the question of what the projection matrix is that projects onto the subspace W and how toapply it to find the desired projection. Second, approach the task in a different way by using the Gram-Schmidtmethod to find an orthonormal basis for subspace W, before then using the resulting basis vectors for theprojection. Last, compare the results obtained from both methods
Plane II is spanned by the vectors:
- (2) · P² - (4)
P1=2
P21
3
Subspace W is spanned by the vectors:
2
W1
- (9) ·
1
W2
1
= (³)
Chapter 11 Solutions
Intermediate Algebra
Ch. 11.1 - For Problems 1-10 answer true or false If 2x+1=23x...Ch. 11.1 - Prob. 2CQCh. 11.1 - Prob. 3CQCh. 11.1 - Prob. 4CQCh. 11.1 - Prob. 5CQCh. 11.1 - Prob. 6CQCh. 11.1 - Prob. 7CQCh. 11.1 - Prob. 8CQCh. 11.1 - Prob. 9CQCh. 11.1 - Prob. 10CQ
Ch. 11.1 - Prob. 1PSCh. 11.1 - Prob. 2PSCh. 11.1 - Prob. 3PSCh. 11.1 - Prob. 4PSCh. 11.1 - Prob. 5PSCh. 11.1 - Prob. 6PSCh. 11.1 - Prob. 7PSCh. 11.1 - Prob. 8PSCh. 11.1 - Prob. 9PSCh. 11.1 - Prob. 10PSCh. 11.1 - Prob. 11PSCh. 11.1 - Prob. 12PSCh. 11.1 - Prob. 13PSCh. 11.1 - Prob. 14PSCh. 11.1 - Prob. 15PSCh. 11.1 - Prob. 16PSCh. 11.1 - Prob. 17PSCh. 11.1 - Prob. 18PSCh. 11.1 - Prob. 19PSCh. 11.1 - Prob. 20PSCh. 11.1 - Prob. 21PSCh. 11.1 - Prob. 22PSCh. 11.1 - Prob. 23PSCh. 11.1 - Prob. 24PSCh. 11.1 - Prob. 25PSCh. 11.1 - Prob. 26PSCh. 11.1 - Prob. 27PSCh. 11.1 - Prob. 28PSCh. 11.1 - Prob. 29PSCh. 11.1 - Prob. 30PSCh. 11.1 - Prob. 31PSCh. 11.1 - Prob. 32PSCh. 11.1 - Prob. 33PSCh. 11.1 - Prob. 34PSCh. 11.1 - Prob. 35PSCh. 11.1 - Prob. 36PSCh. 11.1 - Prob. 37PSCh. 11.1 - Prob. 38PSCh. 11.1 - Prob. 39PSCh. 11.1 - Prob. 40PSCh. 11.1 - Prob. 41PSCh. 11.1 - Prob. 42PSCh. 11.1 - Prob. 43PSCh. 11.1 - Prob. 44PSCh. 11.1 - Prob. 45PSCh. 11.1 - Prob. 46PSCh. 11.1 - Prob. 47PSCh. 11.1 - Prob. 48PSCh. 11.1 - Prob. 49PSCh. 11.1 - Prob. 50PSCh. 11.1 - For Problems 35-52, graph each exponential...Ch. 11.1 - For Problems 35-52, graph each exponential...Ch. 11.1 - Prob. 53PSCh. 11.1 - Prob. 54PSCh. 11.1 - Prob. 55PSCh. 11.1 - Prob. 57PSCh. 11.1 - Prob. 58PSCh. 11.1 - Prob. 59PSCh. 11.1 - Prob. 60PSCh. 11.1 - Prob. 61PSCh. 11.2 - For Problems 1-5, match each type of problem with...Ch. 11.2 - Prob. 2CQCh. 11.2 - Prob. 3CQCh. 11.2 - Prob. 4CQCh. 11.2 - Prob. 5CQCh. 11.2 - Prob. 6CQCh. 11.2 - Prob. 7CQCh. 11.2 - Prob. 8CQCh. 11.2 - Prob. 9CQCh. 11.2 - Prob. 10CQCh. 11.2 - Prob. 1PSCh. 11.2 - Suppose it is estimated that the value of a car...Ch. 11.2 - Prob. 3PSCh. 11.2 - Prob. 4PSCh. 11.2 - Prob. 5PSCh. 11.2 - Prob. 6PSCh. 11.2 - Prob. 7PSCh. 11.2 - Prob. 8PSCh. 11.2 - Prob. 9PSCh. 11.2 - Prob. 10PSCh. 11.2 - Prob. 11PSCh. 11.2 - Prob. 12PSCh. 11.2 - Prob. 13PSCh. 11.2 - Prob. 14PSCh. 11.2 - Prob. 15PSCh. 11.2 - Prob. 16PSCh. 11.2 - Prob. 17PSCh. 11.2 - Prob. 18PSCh. 11.2 - Prob. 19PSCh. 11.2 - Prob. 20PSCh. 11.2 - Prob. 21PSCh. 11.2 - Prob. 22PSCh. 11.2 - Prob. 23PSCh. 11.2 - Prob. 24PSCh. 11.2 - Prob. 25PSCh. 11.2 - Prob. 26PSCh. 11.2 - Prob. 27PSCh. 11.2 - Two years ago Daniel invested some money at 8...Ch. 11.2 - What rate of interest to the nearest hundredth of...Ch. 11.2 - Suppose that a certain radioactive substance has a...Ch. 11.2 - Strontium-90 has a half life of 29 years. If there...Ch. 11.2 - The half life of radium is approximately 1600...Ch. 11.2 - For Problems 33-38, graph each of the exponential...Ch. 11.2 - Prob. 34PSCh. 11.2 - Prob. 35PSCh. 11.2 - Prob. 36PSCh. 11.2 - Prob. 37PSCh. 11.2 - Prob. 38PSCh. 11.2 - For Problems 39-44, express your answer to the...Ch. 11.2 - Prob. 40PSCh. 11.2 - Prob. 41PSCh. 11.2 - Prob. 42PSCh. 11.2 - Prob. 43PSCh. 11.2 - Prob. 44PSCh. 11.2 - Prob. 45PSCh. 11.2 - Prob. 46PSCh. 11.2 - Prob. 47PSCh. 11.2 - Prob. 48PSCh. 11.2 - Prob. 49PSCh. 11.2 - Prob. 50PSCh. 11.2 - Graph f(x)=ex. Now predict the graphs for f(x)=ex,...Ch. 11.2 - Prob. 52PSCh. 11.3 - For Problems 1-10, answer true or false. The...Ch. 11.3 - Prob. 2CQCh. 11.3 - Prob. 3CQCh. 11.3 - Prob. 4CQCh. 11.3 - Prob. 5CQCh. 11.3 - Prob. 6CQCh. 11.3 - Prob. 7CQCh. 11.3 - For Problems 1-10, answer true or false....Ch. 11.3 - Prob. 9CQCh. 11.3 - Prob. 10CQCh. 11.3 - Prob. 1PSCh. 11.3 - Prob. 2PSCh. 11.3 - Prob. 3PSCh. 11.3 - Prob. 4PSCh. 11.3 - Prob. 5PSCh. 11.3 - Prob. 6PSCh. 11.3 - Prob. 7PSCh. 11.3 - Prob. 8PSCh. 11.3 - Prob. 9PSCh. 11.3 - Prob. 10PSCh. 11.3 - Prob. 11PSCh. 11.3 - Prob. 12PSCh. 11.3 - Prob. 13PSCh. 11.3 - Prob. 14PSCh. 11.3 - For Problems 11-20, write each of the following in...Ch. 11.3 - Prob. 16PSCh. 11.3 - Prob. 17PSCh. 11.3 - Prob. 18PSCh. 11.3 - Prob. 19PSCh. 11.3 - Prob. 20PSCh. 11.3 - Prob. 21PSCh. 11.3 - Prob. 22PSCh. 11.3 - Prob. 23PSCh. 11.3 - Prob. 24PSCh. 11.3 - Prob. 25PSCh. 11.3 - Prob. 26PSCh. 11.3 - Prob. 27PSCh. 11.3 - Prob. 28PSCh. 11.3 - Prob. 29PSCh. 11.3 - Prob. 30PSCh. 11.3 - Prob. 31PSCh. 11.3 - Prob. 32PSCh. 11.3 - Prob. 33PSCh. 11.3 - Prob. 34PSCh. 11.3 - Prob. 35PSCh. 11.3 - Prob. 36PSCh. 11.3 - Prob. 37PSCh. 11.3 - Prob. 38PSCh. 11.3 - Prob. 39PSCh. 11.3 - Prob. 40PSCh. 11.3 - Prob. 41PSCh. 11.3 - Prob. 42PSCh. 11.3 - Prob. 43PSCh. 11.3 - Prob. 44PSCh. 11.3 - Prob. 45PSCh. 11.3 - Prob. 46PSCh. 11.3 - Prob. 47PSCh. 11.3 - Prob. 48PSCh. 11.3 - Prob. 49PSCh. 11.3 - Prob. 50PSCh. 11.3 - Prob. 51PSCh. 11.3 - Prob. 52PSCh. 11.3 - Prob. 53PSCh. 11.3 - Prob. 54PSCh. 11.3 - Prob. 55PSCh. 11.3 - Prob. 56PSCh. 11.3 - Prob. 57PSCh. 11.3 - Prob. 58PSCh. 11.3 - Prob. 59PSCh. 11.3 - Prob. 60PSCh. 11.3 - Prob. 61PSCh. 11.3 - Prob. 62PSCh. 11.3 - Prob. 63PSCh. 11.3 - Prob. 64PSCh. 11.3 - Prob. 65PSCh. 11.3 - Prob. 66PSCh. 11.3 - Prob. 67PSCh. 11.3 - Prob. 68PSCh. 11.3 - Prob. 69PSCh. 11.3 - Prob. 70PSCh. 11.3 - Prob. 71PSCh. 11.3 - Prob. 72PSCh. 11.3 - For Problems 69-80, express each of the following...Ch. 11.3 - Prob. 74PSCh. 11.3 - Prob. 75PSCh. 11.3 - Prob. 76PSCh. 11.3 - Prob. 77PSCh. 11.3 - Prob. 78PSCh. 11.3 - Prob. 79PSCh. 11.3 - Prob. 80PSCh. 11.3 - Prob. 81PSCh. 11.3 - Prob. 82PSCh. 11.3 - Prob. 83PSCh. 11.3 - Prob. 84PSCh. 11.3 - Prob. 85PSCh. 11.3 - Prob. 86PSCh. 11.3 - Prob. 87PSCh. 11.3 - Prob. 88PSCh. 11.3 - Prob. 89PSCh. 11.3 - Prob. 90PSCh. 11.3 - Prob. 91PSCh. 11.3 - Prob. 92PSCh. 11.3 - Prob. 93PSCh. 11.3 - Prob. 94PSCh. 11.3 - Prob. 95PSCh. 11.3 - Prob. 96PSCh. 11.3 - Prob. 97PSCh. 11.3 - Prob. 98PSCh. 11.3 - Prob. 99PSCh. 11.3 - Prob. 100PSCh. 11.3 - Prob. 101PSCh. 11.3 - Prob. 102PSCh. 11.4 - For Problems 1-10, answer true or false. The...Ch. 11.4 - Prob. 2CQCh. 11.4 - Prob. 3CQCh. 11.4 - Prob. 4CQCh. 11.4 - Prob. 5CQCh. 11.4 - Prob. 6CQCh. 11.4 - For Problems 1-10, answer true or false. If lnx=1...Ch. 11.4 - Prob. 8CQCh. 11.4 - Prob. 9CQCh. 11.4 - Prob. 10CQCh. 11.4 - Prob. 1PSCh. 11.4 - Prob. 2PSCh. 11.4 - Prob. 3PSCh. 11.4 - Prob. 4PSCh. 11.4 - Prob. 5PSCh. 11.4 - Prob. 6PSCh. 11.4 - Prob. 7PSCh. 11.4 - Prob. 8PSCh. 11.4 - For Problems 1-10, use a calculator to find each...Ch. 11.4 - Prob. 10PSCh. 11.4 - Prob. 11PSCh. 11.4 - Prob. 12PSCh. 11.4 - Prob. 13PSCh. 11.4 - Prob. 14PSCh. 11.4 - Prob. 15PSCh. 11.4 - Prob. 16PSCh. 11.4 - Prob. 17PSCh. 11.4 - Prob. 18PSCh. 11.4 - Prob. 19PSCh. 11.4 - Prob. 20PSCh. 11.4 - Prob. 21PSCh. 11.4 - Prob. 22PSCh. 11.4 - Prob. 23PSCh. 11.4 - Prob. 24PSCh. 11.4 - Prob. 25PSCh. 11.4 - Prob. 26PSCh. 11.4 - Prob. 27PSCh. 11.4 - Prob. 28PSCh. 11.4 - For problems 21-30, use your calculator to find...Ch. 11.4 - Prob. 30PSCh. 11.4 - Prob. 31PSCh. 11.4 - Prob. 32PSCh. 11.4 - Prob. 33PSCh. 11.4 - Prob. 34PSCh. 11.4 - Prob. 35PSCh. 11.4 - Prob. 36PSCh. 11.4 - Prob. 37PSCh. 11.4 - Prob. 38PSCh. 11.4 - Prob. 39PSCh. 11.4 - Prob. 40PSCh. 11.4 - Prob. 41PSCh. 11.4 - Prob. 42PSCh. 11.4 - Prob. 43PSCh. 11.4 - Prob. 44PSCh. 11.4 - Prob. 45PSCh. 11.4 - Prob. 46PSCh. 11.4 - For Problems 47-53, graph each of the functions....Ch. 11.4 - Prob. 48PSCh. 11.4 - Prob. 49PSCh. 11.4 - Prob. 50PSCh. 11.4 - Prob. 51PSCh. 11.4 - Prob. 52PSCh. 11.4 - Prob. 53PSCh. 11.4 - Prob. 54PSCh. 11.4 - Prob. 55PSCh. 11.4 - Prob. 56PSCh. 11.4 - Prob. 57PSCh. 11.4 - Prob. 58PSCh. 11.4 - Prob. 59PSCh. 11.4 - Prob. 60PSCh. 11.4 - Prob. 61PSCh. 11.4 - Why is the number 1 excluded from being a base of...Ch. 11.4 - Prob. 63PSCh. 11.4 - Prob. 64PSCh. 11.4 - Prob. 65PSCh. 11.4 - Prob. 66PSCh. 11.4 - Prob. 67PSCh. 11.4 - Prob. 68PSCh. 11.4 - Prob. 69PSCh. 11.5 - For Problems 1-8, answer true or false. The...Ch. 11.5 - For Problems 1-8, answer true or false. All...Ch. 11.5 - Prob. 3CQCh. 11.5 - Prob. 4CQCh. 11.5 - For Problems 1-8, answer true or false. The...Ch. 11.5 - Prob. 6CQCh. 11.5 - For Problems 1-8, answer true or false. The...Ch. 11.5 - Prob. 8CQCh. 11.5 - Prob. 1PSCh. 11.5 - Prob. 2PSCh. 11.5 - Prob. 3PSCh. 11.5 - Prob. 4PSCh. 11.5 - Prob. 5PSCh. 11.5 - Prob. 6PSCh. 11.5 - For problems 1-14, solve each exponential equation...Ch. 11.5 - For problems 1-14, solve each exponential equation...Ch. 11.5 - For problems 1-14, solve each exponential equation...Ch. 11.5 - For problems 1-14, solve each exponential equation...Ch. 11.5 - Prob. 11PSCh. 11.5 - Prob. 12PSCh. 11.5 - Prob. 13PSCh. 11.5 - Prob. 14PSCh. 11.5 - Prob. 15PSCh. 11.5 - Prob. 16PSCh. 11.5 - Prob. 17PSCh. 11.5 - Prob. 18PSCh. 11.5 - Prob. 19PSCh. 11.5 - Prob. 20PSCh. 11.5 - Prob. 21PSCh. 11.5 - Prob. 22PSCh. 11.5 - Prob. 23PSCh. 11.5 - Prob. 24PSCh. 11.5 - Prob. 25PSCh. 11.5 - Prob. 26PSCh. 11.5 - Prob. 27PSCh. 11.5 - Prob. 28PSCh. 11.5 - Prob. 29PSCh. 11.5 - Prob. 30PSCh. 11.5 - Prob. 31PSCh. 11.5 - Prob. 32PSCh. 11.5 - Prob. 33PSCh. 11.5 - For Problems 33-41, solve each problem and express...Ch. 11.5 - Prob. 35PSCh. 11.5 - Prob. 36PSCh. 11.5 - Prob. 37PSCh. 11.5 - Prob. 38PSCh. 11.5 - Prob. 39PSCh. 11.5 - Prob. 40PSCh. 11.5 - Prob. 41PSCh. 11.5 - Prob. 42PSCh. 11.5 - Prob. 43PSCh. 11.5 - Prob. 44PSCh. 11.5 - Prob. 45PSCh. 11.5 - Prob. 46PSCh. 11.5 - Prob. 47PSCh. 11.5 - Prob. 48PSCh. 11.5 - Prob. 49PSCh. 11.5 - Prob. 50PSCh. 11.5 - Prob. 51PSCh. 11.5 - Prob. 52PSCh. 11.5 - Prob. 53PSCh. 11.5 - Prob. 54PSCh. 11.S - Prob. 1SCh. 11.S - Prob. 2SCh. 11.S - Prob. 3SCh. 11.S - Prob. 4SCh. 11.S - Prob. 5SCh. 11.S - Prob. 6SCh. 11.S - Prob. 7SCh. 11.S - Prob. 8SCh. 11.S - Prob. 9SCh. 11.S - Prob. 10SCh. 11.S - Prob. 11SCh. 11.S - Prob. 12SCh. 11.S - Prob. 13SCh. 11.S - Prob. 14SCh. 11.S - Prob. 15SCh. 11.S - Prob. 16SCh. 11.S - Prob. 17SCh. 11.S - Prob. 18SCh. 11.CR - For problems 1 and 2, graph each of the functions....Ch. 11.CR - Prob. 2CRCh. 11.CR - Prob. 3CRCh. 11.CR - Prob. 4CRCh. 11.CR - Prob. 5CRCh. 11.CR - Prob. 6CRCh. 11.CR - Prob. 7CRCh. 11.CR - Prob. 8CRCh. 11.CR - Prob. 9CRCh. 11.CR - Prob. 10CRCh. 11.CR - Prob. 11CRCh. 11.CR - Prob. 12CRCh. 11.CR - Prob. 13CRCh. 11.CR - For problems 11-14, write each of the following in...Ch. 11.CR - Prob. 15CRCh. 11.CR - Prob. 16CRCh. 11.CR - Prob. 17CRCh. 11.CR - Prob. 18CRCh. 11.CR - Prob. 19CRCh. 11.CR - Prob. 20CRCh. 11.CR - Prob. 21CRCh. 11.CR - Prob. 22CRCh. 11.CR - Prob. 23CRCh. 11.CR - Prob. 24CRCh. 11.CR - Prob. 25CRCh. 11.CR - Prob. 26CRCh. 11.CR - Prob. 27CRCh. 11.CR - Prob. 28CRCh. 11.CR - Prob. 29CRCh. 11.CR - Prob. 30CRCh. 11.CR - Prob. 31CRCh. 11.CR - Prob. 32CRCh. 11.CR - Prob. 33CRCh. 11.CR - Prob. 34CRCh. 11.CR - Prob. 35CRCh. 11.CR - Prob. 36CRCh. 11.CR - Prob. 37CRCh. 11.CR - Prob. 38CRCh. 11.CR - Prob. 39CRCh. 11.CR - Prob. 40CRCh. 11.CR - Prob. 41CRCh. 11.CR - Prob. 42CRCh. 11.CR - Prob. 43CRCh. 11.CR - Prob. 44CRCh. 11.CR - Prob. 45CRCh. 11.CR - Prob. 46CRCh. 11.CR - Prob. 47CRCh. 11.CR - Prob. 48CRCh. 11.CR - Prob. 49CRCh. 11.CR - Prob. 50CRCh. 11.CR - Prob. 51CRCh. 11.CR - Prob. 52CRCh. 11.CR - Suppose that 8000 is invested at 6 interest...Ch. 11.CR - If 25, 000 is invested at 4 interest compounded...Ch. 11.CR - How long will it take 1000 to double itself if it...Ch. 11.CR - Prob. 56CRCh. 11.CR - If 3500 is invested at 8 interest compounded...Ch. 11.CR - Prob. 58CRCh. 11.CR - Prob. 59CRCh. 11.CR - Suppose that a certain radioactive substance has a...Ch. 11.CR - Suppose that the present population of a city is...Ch. 11.CR - Prob. 62CRCh. 11.CR - An earthquake in Mexico in 1985 had and intensity...Ch. 11.CR - Prob. 64CRCh. 11.CT - Prob. 1CTCh. 11.CT - Prob. 2CTCh. 11.CT - Prob. 3CTCh. 11.CT - Prob. 4CTCh. 11.CT - Prob. 5CTCh. 11.CT - Prob. 6CTCh. 11.CT - Prob. 7CTCh. 11.CT - Prob. 8CTCh. 11.CT - Prob. 9CTCh. 11.CT - Prob. 10CTCh. 11.CT - Prob. 11CTCh. 11.CT - Prob. 12CTCh. 11.CT - Prob. 13CTCh. 11.CT - Prob. 14CTCh. 11.CT - Prob. 15CTCh. 11.CT - Prob. 16CTCh. 11.CT - Prob. 17CTCh. 11.CT - Prob. 18CTCh. 11.CT - Prob. 19CTCh. 11.CT - Prob. 20CTCh. 11.CT - Prob. 21CTCh. 11.CT - Prob. 22CTCh. 11.CT - Prob. 23CTCh. 11.CT - Prob. 24CTCh. 11.CT - Prob. 25CT
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