Intermediate Algebra
10th Edition
ISBN: 9781285195728
Author: Jerome E. Kaufmann, Karen L. Schwitters
Publisher: Cengage Learning
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Chapter 8.2, Problem 50PS
To determine
To find:
The equation of the
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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)
show that v3 = (−√3, −3, 3)⊤ is an eigenvector of M3 . Also here find the correspondingeigenvalue λ3 . Just from looking at M3 and its components, can you say something about the remaining twoeigenvalues? If so, what would you say?
find v42 so that v4 = ( 2/5, v42, 1)⊤ is an eigenvector of M4 with corresp. eigenvalue λ4 = 45
Chapter 8 Solutions
Intermediate Algebra
Ch. 8.1 - For Problems 110, answer true or false. The graph...Ch. 8.1 - Prob. 2CQCh. 8.1 - Prob. 3CQCh. 8.1 - Prob. 4CQCh. 8.1 - Prob. 5CQCh. 8.1 - Prob. 6CQCh. 8.1 - Prob. 7CQCh. 8.1 - Prob. 8CQCh. 8.1 - Prob. 9CQCh. 8.1 - Prob. 10CQ
Ch. 8.1 - Prob. 1PSCh. 8.1 - Prob. 2PSCh. 8.1 - Prob. 3PSCh. 8.1 - Prob. 4PSCh. 8.1 - Prob. 5PSCh. 8.1 - Prob. 6PSCh. 8.1 - Prob. 7PSCh. 8.1 - Prob. 8PSCh. 8.1 - Prob. 9PSCh. 8.1 - Prob. 10PSCh. 8.1 - Prob. 11PSCh. 8.1 - Prob. 12PSCh. 8.1 - Prob. 13PSCh. 8.1 - Prob. 14PSCh. 8.1 - Prob. 15PSCh. 8.1 - Prob. 16PSCh. 8.1 - Prob. 17PSCh. 8.1 - Prob. 18PSCh. 8.1 - Prob. 19PSCh. 8.1 - Prob. 20PSCh. 8.1 - Prob. 21PSCh. 8.1 - Prob. 22PSCh. 8.1 - Prob. 23PSCh. 8.1 - Prob. 24PSCh. 8.1 - Prob. 25PSCh. 8.1 - Prob. 26PSCh. 8.1 - Prob. 27PSCh. 8.1 - Prob. 28PSCh. 8.1 - Prob. 29PSCh. 8.1 - Prob. 30PSCh. 8.1 - Prob. 31PSCh. 8.1 - Prob. 32PSCh. 8.1 - Prob. 33PSCh. 8.1 - Prob. 34PSCh. 8.1 - Prob. 35PSCh. 8.1 - Prob. 36PSCh. 8.1 - Prob. 37PSCh. 8.1 - Prob. 38PSCh. 8.1 - Prob. 39PSCh. 8.2 - Prob. 1CQCh. 8.2 - Prob. 2CQCh. 8.2 - Prob. 3CQCh. 8.2 - Prob. 4CQCh. 8.2 - Prob. 5CQCh. 8.2 - Prob. 6CQCh. 8.2 - Prob. 7CQCh. 8.2 - Prob. 8CQCh. 8.2 - Prob. 9CQCh. 8.2 - Prob. 10CQCh. 8.2 - Prob. 1PSCh. 8.2 - Prob. 2PSCh. 8.2 - Prob. 3PSCh. 8.2 - Prob. 4PSCh. 8.2 - Prob. 5PSCh. 8.2 - Prob. 6PSCh. 8.2 - Prob. 7PSCh. 8.2 - Prob. 8PSCh. 8.2 - Prob. 9PSCh. 8.2 - Prob. 10PSCh. 8.2 - Prob. 11PSCh. 8.2 - Prob. 12PSCh. 8.2 - Prob. 13PSCh. 8.2 - Prob. 14PSCh. 8.2 - Prob. 15PSCh. 8.2 - Prob. 16PSCh. 8.2 - Prob. 17PSCh. 8.2 - Prob. 18PSCh. 8.2 - Prob. 19PSCh. 8.2 - Prob. 20PSCh. 8.2 - Prob. 21PSCh. 8.2 - Prob. 22PSCh. 8.2 - Prob. 23PSCh. 8.2 - Prob. 24PSCh. 8.2 - Prob. 25PSCh. 8.2 - Prob. 26PSCh. 8.2 - Prob. 27PSCh. 8.2 - Prob. 28PSCh. 8.2 - Prob. 29PSCh. 8.2 - Prob. 30PSCh. 8.2 - Prob. 31PSCh. 8.2 - Prob. 32PSCh. 8.2 - Prob. 33PSCh. 8.2 - Prob. 34PSCh. 8.2 - Prob. 35PSCh. 8.2 - Prob. 36PSCh. 8.2 - Prob. 37PSCh. 8.2 - Prob. 38PSCh. 8.2 - Prob. 39PSCh. 8.2 - Prob. 40PSCh. 8.2 - Prob. 41PSCh. 8.2 - Prob. 42PSCh. 8.2 - Prob. 43PSCh. 8.2 - Prob. 44PSCh. 8.2 - Prob. 45PSCh. 8.2 - Prob. 46PSCh. 8.2 - Prob. 47PSCh. 8.2 - Prob. 48PSCh. 8.2 - Prob. 49PSCh. 8.2 - Prob. 50PSCh. 8.2 - Prob. 51PSCh. 8.2 - Prob. 52PSCh. 8.2 - Prob. 53PSCh. 8.2 - Prob. 54PSCh. 8.2 - Prob. 55PSCh. 8.2 - Prob. 56PSCh. 8.2 - Prob. 57PSCh. 8.2 - Prob. 58PSCh. 8.2 - Prob. 59PSCh. 8.2 - Prob. 60PSCh. 8.2 - Prob. 61PSCh. 8.2 - Prob. 62PSCh. 8.2 - Prob. 63.1PSCh. 8.2 - By expanding (xh)2+(yk)2=r2, we obtain...Ch. 8.2 - Prob. 63.3PSCh. 8.2 - Prob. 63.4PSCh. 8.2 - Prob. 63.5PSCh. 8.2 - Prob. 63.6PSCh. 8.2 - Prob. 64PSCh. 8.2 - Prob. 65PSCh. 8.2 - Prob. 66.1PSCh. 8.2 - Prob. 66.2PSCh. 8.2 - Prob. 66.3PSCh. 8.2 - Prob. 66.4PSCh. 8.2 - Prob. 66.5PSCh. 8.2 - Prob. 66.6PSCh. 8.3 - Prob. 1CQCh. 8.3 - Prob. 2CQCh. 8.3 - Prob. 3CQCh. 8.3 - Prob. 4CQCh. 8.3 - Prob. 5CQCh. 8.3 - Prob. 6CQCh. 8.3 - Prob. 7CQCh. 8.3 - Prob. 8CQCh. 8.3 - Prob. 9CQCh. 8.3 - Prob. 10CQCh. 8.3 - Prob. 1PSCh. 8.3 - Prob. 2PSCh. 8.3 - Prob. 3PSCh. 8.3 - Prob. 4PSCh. 8.3 - Prob. 5PSCh. 8.3 - Prob. 6PSCh. 8.3 - Prob. 7PSCh. 8.3 - Prob. 8PSCh. 8.3 - Prob. 9PSCh. 8.3 - Prob. 10PSCh. 8.3 - Prob. 11PSCh. 8.3 - Prob. 12PSCh. 8.3 - Prob. 13PSCh. 8.3 - Prob. 14PSCh. 8.3 - Prob. 15PSCh. 8.3 - Prob. 16PSCh. 8.3 - Prob. 17PSCh. 8.3 - Prob. 18PSCh. 8.3 - Prob. 19PSCh. 8.3 - Prob. 20PSCh. 8.3 - Prob. 21PSCh. 8.3 - Prob. 22PSCh. 8.3 - Prob. 23PSCh. 8.3 - Prob. 24PSCh. 8.3 - Prob. 25PSCh. 8.3 - Prob. 26PSCh. 8.3 - Prob. 27PSCh. 8.3 - Prob. 28PSCh. 8.3 - Prob. 29PSCh. 8.3 - Prob. 30PSCh. 8.4 - Prob. 1CQCh. 8.4 - Prob. 2CQCh. 8.4 - Prob. 3CQCh. 8.4 - Prob. 4CQCh. 8.4 - Prob. 5CQCh. 8.4 - Prob. 6CQCh. 8.4 - Prob. 7CQCh. 8.4 - Prob. 8CQCh. 8.4 - Prob. 9CQCh. 8.4 - Prob. 10CQCh. 8.4 - Prob. 1PSCh. 8.4 - Prob. 2PSCh. 8.4 - Prob. 3PSCh. 8.4 - Prob. 4PSCh. 8.4 - Prob. 5PSCh. 8.4 - Prob. 6PSCh. 8.4 - Prob. 7PSCh. 8.4 - Prob. 8PSCh. 8.4 - Prob. 9PSCh. 8.4 - Prob. 10PSCh. 8.4 - Prob. 11PSCh. 8.4 - Prob. 12PSCh. 8.4 - Prob. 13PSCh. 8.4 - Prob. 14PSCh. 8.4 - Prob. 15PSCh. 8.4 - Prob. 16PSCh. 8.4 - Prob. 17PSCh. 8.4 - Prob. 18PSCh. 8.4 - Prob. 19PSCh. 8.4 - Prob. 20PSCh. 8.4 - Prob. 21PSCh. 8.4 - Prob. 22PSCh. 8.4 - Prob. 23PSCh. 8.4 - Prob. 24PSCh. 8.4 - Prob. 25PSCh. 8.4 - Prob. 26PSCh. 8.4 - Prob. 27PSCh. 8.4 - Prob. 28PSCh. 8.4 - Prob. 29PSCh. 8.4 - Prob. 30PSCh. 8.4 - Prob. 31PSCh. 8.4 - Prob. 32PSCh. 8.4 - Prob. 33PSCh. 8.4 - Prob. 34PSCh. 8.4 - Prob. 35PSCh. 8.4 - Prob. 36PSCh. 8.4 - Prob. 37PSCh. 8.4 - Prob. 38PSCh. 8.4 - Prob. 39PSCh. 8.4 - Prob. 40.1PSCh. 8.4 - Prob. 40.2PSCh. 8.4 - Prob. 40.3PSCh. 8.4 - Prob. 40.4PSCh. 8.4 - Prob. 40.5PSCh. 8.4 - Prob. 40.6PSCh. 8.4 - Prob. 41.1PSCh. 8.4 - Prob. 41.2PSCh. 8.4 - Prob. 41.3PSCh. 8.4 - Prob. 41.4PSCh. 8.4 - Prob. 41.5PSCh. 8.4 - Prob. 41.6PSCh. 8.4 - Prob. 41.7PSCh. 8.4 - Prob. 41.8PSCh. 8.4 - Prob. 41.9PSCh. 8.4 - Prob. 41.10PSCh. 8.4 - Prob. 42PSCh. 8.S - Prob. 1SCh. 8.S - Prob. 2SCh. 8.S - Prob. 3SCh. 8.S - Prob. 4SCh. 8.S - Prob. 5SCh. 8.S - Prob. 6SCh. 8.S - Prob. 7SCh. 8.S - Prob. 8SCh. 8.CR - Prob. 1CRCh. 8.CR - Prob. 2CRCh. 8.CR - Prob. 3CRCh. 8.CR - Prob. 4CRCh. 8.CR - Prob. 5CRCh. 8.CR - Prob. 6CRCh. 8.CR - Prob. 7CRCh. 8.CR - Prob. 8CRCh. 8.CR - Prob. 9CRCh. 8.CR - Prob. 10CRCh. 8.CR - Prob. 11CRCh. 8.CR - Prob. 12CRCh. 8.CR - Prob. 13CRCh. 8.CR - Prob. 14CRCh. 8.CR - Prob. 15CRCh. 8.CR - Prob. 16CRCh. 8.CR - Prob. 17CRCh. 8.CR - Prob. 18CRCh. 8.CR - Prob. 19CRCh. 8.CR - Prob. 20CRCh. 8.CR - Prob. 21CRCh. 8.CR - Prob. 22CRCh. 8.CR - Prob. 23CRCh. 8.CR - Prob. 24CRCh. 8.CR - Prob. 25CRCh. 8.CR - Prob. 26CRCh. 8.CR - Prob. 27CRCh. 8.CR - Prob. 28CRCh. 8.CR - Prob. 29CRCh. 8.CR - Prob. 30CRCh. 8.CR - Prob. 31CRCh. 8.CR - Prob. 32CRCh. 8.CR - Prob. 33CRCh. 8.CR - For Problems 3150, graph each equation....Ch. 8.CR - Prob. 35CRCh. 8.CR - Prob. 36CRCh. 8.CR - Prob. 37CRCh. 8.CR - Prob. 38CRCh. 8.CR - Prob. 39CRCh. 8.CR - Prob. 40CRCh. 8.CR - Prob. 41CRCh. 8.CR - Prob. 42CRCh. 8.CR - Prob. 43CRCh. 8.CR - Prob. 44CRCh. 8.CR - Prob. 45CRCh. 8.CR - Prob. 46CRCh. 8.CR - Prob. 47CRCh. 8.CR - Prob. 48CRCh. 8.CR - Prob. 49CRCh. 8.CR - Prob. 50CRCh. 8.CT - Prob. 1CTCh. 8.CT - Prob. 2CTCh. 8.CT - Prob. 3CTCh. 8.CT - Prob. 4CTCh. 8.CT - Prob. 5CTCh. 8.CT - Prob. 6CTCh. 8.CT - Prob. 7CTCh. 8.CT - Prob. 12CTCh. 8.CT - Prob. 13CTCh. 8.CT - Prob. 14CTCh. 8.CT - Prob. 15CTCh. 8.CT - Prob. 16CTCh. 8.CT - Prob. 17CTCh. 8.CT - Prob. 18CTCh. 8.CT - Prob. 19CTCh. 8.CT - Prob. 20CTCh. 8.CT - Prob. 21CTCh. 8.CT - Prob. 22CTCh. 8.CT - Prob. 23CTCh. 8.CT - Prob. 24CTCh. 8.CT - Prob. 25CTCh. 8.CM - Prob. 1CMCh. 8.CM - Prob. 2CMCh. 8.CM - Prob. 3CMCh. 8.CM - Prob. 4CMCh. 8.CM - Prob. 5CMCh. 8.CM - Prob. 6CMCh. 8.CM - Prob. 7CMCh. 8.CM - Prob. 8CMCh. 8.CM - Prob. 9CMCh. 8.CM - Prob. 10CMCh. 8.CM - Prob. 11CMCh. 8.CM - Prob. 12CMCh. 8.CM - Prob. 13CMCh. 8.CM - Prob. 14CMCh. 8.CM - Prob. 15CMCh. 8.CM - Prob. 16CMCh. 8.CM - Prob. 17CMCh. 8.CM - Prob. 18CMCh. 8.CM - Prob. 19CMCh. 8.CM - Prob. 20CMCh. 8.CM - Prob. 21CMCh. 8.CM - Prob. 22CMCh. 8.CM - Prob. 23CMCh. 8.CM - Prob. 24CMCh. 8.CM - Prob. 25CMCh. 8.CM - Prob. 26CMCh. 8.CM - Prob. 27CMCh. 8.CM - Prob. 28CMCh. 8.CM - Prob. 29CMCh. 8.CM - Prob. 30CMCh. 8.CM - Prob. 31CMCh. 8.CM - Prob. 32CMCh. 8.CM - Prob. 33CMCh. 8.CM - Prob. 34CMCh. 8.CM - Prob. 35CMCh. 8.CM - Prob. 36CMCh. 8.CM - Prob. 37CMCh. 8.CM - Prob. 38CMCh. 8.CM - Prob. 39CMCh. 8.CM - Prob. 40CMCh. 8.CM - Prob. 41CMCh. 8.CM - Prob. 42CMCh. 8.CM - Prob. 43CMCh. 8.CM - Prob. 44CMCh. 8.CM - Prob. 45CMCh. 8.CM - Prob. 46CMCh. 8.CM - Prob. 47CMCh. 8.CM - Prob. 48CMCh. 8.CM - Prob. 49CMCh. 8.CM - Prob. 50CMCh. 8.CM - Prob. 51CMCh. 8.CM - Prob. 52CMCh. 8.CM - Prob. 53CMCh. 8.CM - Prob. 54CMCh. 8.CM - Prob. 55CMCh. 8.CM - Prob. 56CMCh. 8.CM - For Problems 5564, solve inequality and express...Ch. 8.CM - Prob. 58CMCh. 8.CM - Prob. 59CMCh. 8.CM - Prob. 60CMCh. 8.CM - Prob. 61CMCh. 8.CM - Prob. 62CMCh. 8.CM - Prob. 63CMCh. 8.CM - Prob. 64CMCh. 8.CM - Prob. 65CMCh. 8.CM - For Problems 65-70, graph the following equations....Ch. 8.CM - Prob. 67CMCh. 8.CM - Prob. 68CMCh. 8.CM - Prob. 69CMCh. 8.CM - Prob. 70CMCh. 8.CM - Prob. 71CMCh. 8.CM - Prob. 72CMCh. 8.CM - Prob. 73CMCh. 8.CM - Prob. 74CMCh. 8.CM - Prob. 75CMCh. 8.CM - Prob. 76CMCh. 8.CM - Prob. 77CMCh. 8.CM - Prob. 78CMCh. 8.CM - Prob. 79CMCh. 8.CM - Prob. 80CMCh. 8.CM - Prob. 81CMCh. 8.CM - Prob. 82CMCh. 8.CM - Prob. 83CMCh. 8.CM - Prob. 84CMCh. 8.CM - Prob. 85CMCh. 8.CM - Prob. 86CMCh. 8.CM - Prob. 87CMCh. 8.CM - Prob. 88CM
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