Elementary Algebra
17th Edition
ISBN: 9780998625713
Author: Lynn Marecek, MaryAnne Anthony-Smith
Publisher: OpenStax - Rice University
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Textbook Question
Chapter 2, Problem 578RE
In the following exercises, solve each linear equation.
578.
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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
Chapter 2 Solutions
Elementary Algebra
Ch. 2.1 - Is y=43 a solution of 9y+2=6y+3 ?Ch. 2.1 - Is y=75 a solution of 5y+3=10y4 ?Ch. 2.1 - Solve: x+19=27 .Ch. 2.1 - Solve: x+16=34 .Ch. 2.1 - Solve: n61=75 .Ch. 2.1 - Solve: p41=73 .Ch. 2.1 - Solve: p23=56 .Ch. 2.1 - Solve: q12=56 .Ch. 2.1 - Solve: b0.47=2.1 .Ch. 2.1 - Solve: c0.93=4.6 .
Ch. 2.1 - Solve: 8y47y7=4 .Ch. 2.1 - Solve: 6z+55z4=3 .Ch. 2.1 - Solve: 5(p3)4p=10 .Ch. 2.1 - Solve: 4(q+2)3q=8 .Ch. 2.1 - Solve: 4(2h3)7h=6(h2)6(h1) .Ch. 2.1 - Solve: 2(5x+2)9x=3(x2)3(x4) .Ch. 2.1 - Translate and solve: Ten more than x is equal to...Ch. 2.1 - Translate and solve: Twelve less than x is equal...Ch. 2.1 - Translate and solve: The difference of 4x and 3x...Ch. 2.1 - Translate and solve: The difference of 7a and 6a...Ch. 2.1 - Translate into an algebraic equation and solve:...Ch. 2.1 - Translate into an algebraic equation and solve:...Ch. 2.1 - Translate into an algebraic equation and solve:...Ch. 2.1 - Translate into an algebraic equation and solve:...Ch. 2.1 - In the following exercises, determine whether the...Ch. 2.1 - In the following exercises, determine whether the...Ch. 2.1 - In the following exercises, determine whether the...Ch. 2.1 - In the following exercises, determine whether the...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation....Ch. 2.1 - In the following exercises, solve each equation....Ch. 2.1 - In the following exercises, solve each equation....Ch. 2.1 - In the following exercises, solve each equation....Ch. 2.1 - In the following exercises, solve each equation....Ch. 2.1 - In the following exercises, solve each equation....Ch. 2.1 - In the following exercises, solve each equation....Ch. 2.1 - In the following exercises, solve each equation....Ch. 2.1 - In the following exercises, solve each equation....Ch. 2.1 - In the following exercises, solve each equation....Ch. 2.1 - In the following exercises, solve each equation....Ch. 2.1 - In the following exercises, solve each equation....Ch. 2.1 - In the following exercises, solve each equation....Ch. 2.1 - In the following exercises, solve each equation....Ch. 2.1 - In the following exercises, solve each equation....Ch. 2.1 - In the following exercises, solve each equation....Ch. 2.1 - In the following exercises, solve each equation....Ch. 2.1 - In the following exercises, solve each equation....Ch. 2.1 - In the following exercises, solve each equation....Ch. 2.1 - In the following exercises, solve each equation....Ch. 2.1 - In the following exercises, solve each equation....Ch. 2.1 - In the following exercises, solve each equation....Ch. 2.1 - In the following exercises, translate to an...Ch. 2.1 - In the following exercises, translate to an...Ch. 2.1 - In the following exercises, translate to an...Ch. 2.1 - In the following exercises, translate to an...Ch. 2.1 - In the following exercises, translate to an...Ch. 2.1 - In the following exercises, translate to an...Ch. 2.1 - In the following exercises, translate to an...Ch. 2.1 - 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How do...Ch. 2.1 - What is the first step in your solution to the...Ch. 2.2 - Solve: 3y=41 .Ch. 2.2 - Solve: 4z=55 .Ch. 2.2 - Solve: a7=42 .Ch. 2.2 - Solve: b6=24 .Ch. 2.2 - Solve: k=8 .Ch. 2.2 - Solve: g=3 .Ch. 2.2 - Solve: 25n=14 .Ch. 2.2 - Solve: 56y=15 .Ch. 2.2 - Solve: 925=45z .Ch. 2.2 - Solve: 56=83r .Ch. 2.2 - Solve: 1827=15c9c3c .Ch. 2.2 - Solve: 1822=12xx4x .Ch. 2.2 - Solve: 4(q2)8=24 .Ch. 2.2 - Solve: 6(r2)12=30 .Ch. 2.2 - Translate and solve: The number 132 is the product...Ch. 2.2 - Translate and solve: The number 117 is the product...Ch. 2.2 - Translate and solve: n divided by 7 is equal to 21...Ch. 2.2 - Translate and solve: n divided by 8 is equal to 56...Ch. 2.2 - Translate and solve: The quotient of q and 8 is...Ch. 2.2 - Translate and solve: The quotient of p and 9 is...Ch. 2.2 - Translate and solve: Two-fifths of f is 16.Ch. 2.2 - Translate and solve: Three-fourths of f is 21.Ch. 2.2 - Translate and solve: The sum of five-eighths and x...Ch. 2.2 - Translate and solve: The sum of three-fourths and...Ch. 2.2 - Translate and solve: Arianna bought a 24-pack of...Ch. 2.2 - Translate and solve: At JB’s Bowling Alley, 6...Ch. 2.2 - Translate and solve: The annual property tax on...Ch. 2.2 - Translate and solve: Stella planted 14 flats of...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - 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In the following exercises, solve each equation....Ch. 2.2 - In the following exercises, solve each equation....Ch. 2.2 - In the following exercises, solve each equation....Ch. 2.2 - In the following exercises, solve each equation....Ch. 2.2 - In the following exercises, solve each equation....Ch. 2.2 - In the following exercises, solve each equation....Ch. 2.2 - In the following exercises, solve each equation....Ch. 2.2 - In the following exercises, solve each equation....Ch. 2.2 - In the following exercises, solve each equation....Ch. 2.2 - In the following exercises, solve each equation....Ch. 2.2 - In the following exercises, solve each equation....Ch. 2.2 - In the following exercises, solve each equation....Ch. 2.2 - In the following exercises, solve each equation....Ch. 2.2 - In the following exercises, solve each equation....Ch. 2.2 - In the following exercises, solve each equation....Ch. 2.2 - In the following exercises, solve each equation....Ch. 2.2 - In the following exercises, solve each equation....Ch. 2.2 - In the following exercises, solve each equation....Ch. 2.2 - In the following exercises, translate to an...Ch. 2.2 - In the following exercises, translate to an...Ch. 2.2 - In the following exercises, translate to an...Ch. 2.2 - In the following exercises, translate to an...Ch. 2.2 - In the following exercises, translate to an...Ch. 2.2 - In the following exercises, translate to an...Ch. 2.2 - In the following exercises, translate to an...Ch. 2.2 - In the following exercises, translate to an...Ch. 2.2 - In the following exercises, translate to an...Ch. 2.2 - In the following exercises, translate to an...Ch. 2.2 - In the following exercises, translate to an...Ch. 2.2 - In the following exercises, translate to an...Ch. 2.2 - In the following exercises, translate to an...Ch. 2.2 - In the following exercises, translate to an...Ch. 2.2 - In the following exercises, translate to an...Ch. 2.2 - In the following exercises, translate to an...Ch. 2.2 - In the following exercises, translate to an...Ch. 2.2 - In the following exercises, translate to an...Ch. 2.2 - In the following exercises, translate to an...Ch. 2.2 - In the following exercises, translate to an...Ch. 2.2 - In the following exercises, translate into an...Ch. 2.2 - In the following exercises, translate into an...Ch. 2.2 - In the following exercises, translate into an...Ch. 2.2 - In the following exercises, translate into an...Ch. 2.2 - In the following exercises, translate into an...Ch. 2.2 - In the following exercises, translate into an...Ch. 2.2 - In the following exercises, translate into an...Ch. 2.2 - In the following exercises, translate into an...Ch. 2.2 - Commission Every week Perry gets paid $150 plus...Ch. 2.2 - Stamps Travis bought $9.45 worth of 49-cent stamps...Ch. 2.2 - Frida started to solve the equation 3x=36 by...Ch. 2.2 - Emiliano thinks x=40 is the solution to the...Ch. 2.3 - Solve: 3x+4=8 .Ch. 2.3 - Solve: 5a+3=37 .Ch. 2.3 - Solve: 5y9=16 .Ch. 2.3 - Solve: 3m8=19 .Ch. 2.3 - Solve: 6n=5n10 .Ch. 2.3 - Solve: 6c=7c1 .Ch. 2.3 - Solve: 3p14=5p .Ch. 2.3 - Solve: 8m+9=5m .Ch. 2.3 - Solve: 12j=4j+32 .Ch. 2.3 - Solve: 8h=4h+12 .Ch. 2.3 - Solve: 12x+8=6x+2 .Ch. 2.3 - Solve: 9y+4=7y+12 .Ch. 2.3 - Solve: 8q5=4q+7 .Ch. 2.3 - Solve: 7n3=n+3 .Ch. 2.3 - Solve: 2a2=6a+18 .Ch. 2.3 - Solve: 4k1=7k+17 .Ch. 2.3 - Solve: 78x12=18x2 .Ch. 2.3 - Solve: 76y+11=16y+8 .Ch. 2.3 - Solve: 2.8x+12=1.4x9 .Ch. 2.3 - Solve: 3.6y+8=1.2y4 .Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - 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How...Ch. 2.4 - Solve: 5(x+3)=35 .Ch. 2.4 - Solve: 6(y4)=18 .Ch. 2.4 - Solve: (y+8)=2 .Ch. 2.4 - Solve: (z+4)=12 .Ch. 2.4 - Solve: 2(m4)+3=1 .Ch. 2.4 - Solve: 7(n3)8=15 .Ch. 2.4 - Solve: 13(6u+3)=7u .Ch. 2.4 - Solve: 23(9x12)=8+2x .Ch. 2.4 - Solve: 123(4j+3)=17 .Ch. 2.4 - Solve: 68(k2)=10 .Ch. 2.4 - Solve: 6(p3)7=5(4p+3)12 .Ch. 2.4 - Solve: 8(q+1)5=3(2q4)1 .Ch. 2.4 - Solve: 6[42(7y1)]=8(138y) .Ch. 2.4 - Solve: 12[15(4z1)]=3(24+11z) .Ch. 2.4 - Solve: 0.55(100n+8)=0.6(85n+14) .Ch. 2.4 - Solve: 0.15(40m120)=0.5(60m+12) .Ch. 2.4 - Classify the equation as a conditional equation,...Ch. 2.4 - Classify the equation as a conditional equation,...Ch. 2.4 - Classify the equation as a conditional equation,...Ch. 2.4 - Classify the equation as a conditional equation,...Ch. 2.4 - Classify the equation as a conditional equation,...Ch. 2.4 - Classify the equation as a conditional equation,...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - 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In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, classify each equation...Ch. 2.4 - In the following exercises, classify each equation...Ch. 2.4 - In the following exercises, classify each equation...Ch. 2.4 - In the following exercises, classify each equation...Ch. 2.4 - In the following exercises, classify each equation...Ch. 2.4 - In the following exercises, classify each equation...Ch. 2.4 - In the following exercises, classify each equation...Ch. 2.4 - In the following exercises, classify each equation...Ch. 2.4 - In the following exercises, classify each equation...Ch. 2.4 - In the following exercises, classify each equation...Ch. 2.4 - In the following exercises, classify each equation...Ch. 2.4 - In the following exercises, classify each equation...Ch. 2.4 - In the following exercises, classify each equation...Ch. 2.4 - In the following exercises, classify each equation...Ch. 2.4 - In the following exercises, classify each equation...Ch. 2.4 - In the following exercises, classify each equation...Ch. 2.4 - In the following exercises, classify each equation...Ch. 2.4 - In the following exercises, classify each equation...Ch. 2.4 - In the following exercises, classify each equation...Ch. 2.4 - In the following exercises, classify each equation...Ch. 2.4 - Fencing Micah has 44 feet of fencing to make a dog...Ch. 2.4 - Coins Rhonda has $1.90 in nickels and dimes. The...Ch. 2.4 - Using your own words, list the steps in the...Ch. 2.4 - Explain why you should simplify both sides of an...Ch. 2.4 - What is the first step you take when solving the...Ch. 2.4 - Solve the equation 14(8x+20)=3x4 explaining all...Ch. 2.5 - Solve: 14x+12=58 .Ch. 2.5 - Solve: 18x+12=14 .Ch. 2.5 - Solve: 7=12x+34x23x .Ch. 2.5 - Solve: 1=12u+14u23u .Ch. 2.5 - Solve: x+13=16x12 .Ch. 2.5 - Solve: c+34=12c14 .Ch. 2.5 - Solve: 11=12(6p+2) .Ch. 2.5 - Solve: 8=13(9q+6) .Ch. 2.5 - Solve: 15(n+3)=14(n+2) .Ch. 2.5 - Solve: 12(m3)=14(m7) .Ch. 2.5 - Solve: 4y73=y6 .Ch. 2.5 - Solve: 2z54=z8 .Ch. 2.5 - Solve: b10+2=b4+5 .Ch. 2.5 - Solve: c6+3=c3+4 .Ch. 2.5 - Solve: 3r+56+1=4r+33 .Ch. 2.5 - Solve: 2s+32+1=3s+24 .Ch. 2.5 - Solve: 0.14h+0.12=0.35h2.4 .Ch. 2.5 - Solve: 0.65k0.1=0.4k0.35 .Ch. 2.5 - Solve: 0.25n+0.05(n+5)=2.95 .Ch. 2.5 - Solve: 0.10d+0.05(d5)=2.15 .Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - In the following exercises, solve each equation...Ch. 2.5 - Coins Taylor has $2.00 in dimes and pennies. 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