Intermediate Algebra (12th Edition)
12th Edition
ISBN: 9780321924711
Author: Marvin L. Bittinger
Publisher: PEARSON
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Chapter B, Problem 32ES
c Solve using Cramer’s rule.
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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 B Solutions
Intermediate Algebra (12th Edition)
Ch. B - Evaluate. [3241]Ch. B - Evaluate.
2.
Ch. B - Evaluate.
3.
Ch. B - Evaluate.
4.
Ch. B - 5. Solve using Cramer’s rule:
Ch. B - 6. Solve using Cramer’s rule:
Ch. B - a Evaluate. [3728]Ch. B - a Evaluate. [5445]Ch. B - a Evaluate.
3.
Ch. B - a Evaluate. [4579]
Ch. B - a Evaluate.
5.
Ch. B - a Evaluate.
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Ch. B - a Evaluate.
7.
Ch. B - a Evaluate.
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Ch. B - b Evaluate.
9.
Ch. B - b Evaluate. [302512201]Ch. B - b Evaluate. [123342012]Ch. B - b Evaluate. [122210331]Ch. B - b Evaluate. [322214433]Ch. B - b Evaluate.
14.
Ch. B - b Evaluate.
15.
Ch. B - b Evaluate. [1652445310]Ch. B - c Solve using Cramers rule. x4y=6,5x+9y=10Ch. B - c Solve using Cramer’s rule.
18.
Ch. B - c Solve using Cramer’s rule.
19.
Ch. B - c Solve using Cramers rule. 5x4y=3,7x+2y=6Ch. B - c Solve using Cramers rule. 4x+2y=11,3xy=2Ch. B - c Solve using Cramers rule. 3x3y=11,9x2y=5Ch. B - c Solve using Cramers rule. x+4y=8,3x+5y=3Ch. B - c Solve using Cramers rule. x+4y=5,3x+2y=13Ch. B - c Solve using Cramers rule....Ch. B - c Solve using Cramers rule....Ch. B - c Solve using Cramers rule....Ch. B - c Solve using Cramers rule. 3c=6,b+2c=2,7a3b5c=14Ch. B - c Solve using Cramer’s rule.
29.
Ch. B - c Solve using Cramers rule....Ch. B - c Solve using Cramers rule....Ch. B - c Solve using Cramers rule....
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- Q1: A: Let M and N be two subspace of finite dimension linear space X, show that if M = N then dim M = dim N but the converse need not to be true. B: Let A and B two balanced subsets of a linear space X, show that whether An B and AUB are balanced sets or nor. Q2: Answer only two A:Let M be a subset of a linear space X, show that M is a hyperplane of X iff there exists ƒ€ X'/{0} and a € F such that M = (x = x/f&x) = x}. fe B:Show that every two norms on finite dimension linear space are equivalent C: Let f be a linear function from a normed space X in to a normed space Y, show that continuous at x, E X iff for any sequence (x) in X converge to Xo then the sequence (f(x)) converge to (f(x)) in Y. Q3: A:Let M be a closed subspace of a normed space X, constract a linear space X/M as normed space B: Let A be a finite dimension subspace of a Banach space X, show that A is closed. C: Show that every finite dimension normed space is Banach space.arrow_forward• Plane II is spanned by the vectors: P12 P2 = 1 • Subspace W is spanned by the vectors: W₁ = -- () · 2 1 W2 = 0arrow_forwardThree streams - Stream A, Stream B, and Stream C - flow into a lake. The flow rates of these streams are not yet known and thus to be found. The combined water inflow from the streams is 300 m³/h. The rate of Stream A is three times the combined rates of Stream B and Stream C. The rate of Stream B is 50 m³/h less than half of the difference between the rates of Stream A and Stream C. Find the flow rates of the three streams by setting up an equation system Ax = b and solving it for x. Provide the values of A and b. Assuming that you get to an upper-triangular matrix U using an elimination matrix E such that U = E A, provide also the components of E.arrow_forward
- dent Application X GA spinner is divided into five cox | + 9/26583471/4081d162951bfdf39e254aa2151384b7 A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below: Spinner Results Color Frequency Red 5 Blue 11 Green 18 Yellow 5 Purple 7 Based on these results, express the probability that the next spin will land on purple as a fraction in simplest form. Answer Attempt 1 out of 2 Submit Answer 0 Feb 12 10:11 Oarrow_forward2 5x + 2–49 2 x+10x+21arrow_forward5x 2x+y+ 3x + 3y 4 6arrow_forward
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