Elementary Linear Algebra: Applications Version
12th Edition
ISBN: 9781119282365
Author: Howard Anton, Chris Rorres, Anton Kaul
Publisher: WILEY
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Chapter 4 Solutions
Elementary Linear Algebra: Applications Version
Ch. 4.1 - Let V be the set of all ordered pairs of real...Ch. 4.1 - Let V be the set of all ordered pairs of real...Ch. 4.1 - In Exercises 312, determine whether each set...Ch. 4.1 - In Exercises 312, determine whether each set...Ch. 4.1 - In Exercises 312, determine whether each set...Ch. 4.1 - In Exercises 312, determine whether each set...Ch. 4.1 - In Exercises 312, determine whether each set...Ch. 4.1 - In Exercises 312, determine whether each set...Ch. 4.1 - Verify Axioms 3, 7, 8, and 9 for the vector space...Ch. 4.2 - In Exercises 12, use the Subspace Test to...
Ch. 4.2 - In Exercises 12, use the Subspace Test to...Ch. 4.2 - In Exercises 34, use the Subspace Test to...Ch. 4.2 - In Exercises 56, use the Subspace Test to...Ch. 4.2 - In Exercises 78, use the Subspace Test to...Ch. 4.2 - In Exercises 78, use the Subspace Test to...Ch. 4.2 - In Exercises 1112, use the Subspace Test to...Ch. 4.2 - In Exercises 1112, use the Subspace Test to...Ch. 4.2 - In Exercises 1314, use the Subspace Test to...Ch. 4.2 - In Exercises 1516, use the Subspace Test to...Ch. 4.2 - In parts (a)(h) determine whether the statement is...Ch. 4.3 - Which of the following are linear combinations of...Ch. 4.3 - Express the following as linear combinations of u...Ch. 4.3 - Prove that if {u, v} spans the vector space V,...Ch. 4.4 - Explain why the following form linearly dependent...Ch. 4.4 - In each part, determine whether the vectors are...Ch. 4.4 - In each part, determine whether the vectors are...Ch. 4.4 - In each part, determine whether the vectors are...Ch. 4.4 - In each part, determine whether the matrices are...Ch. 4.4 - a. Show that the three vectors v1 = (0, 3, 1, 1),...Ch. 4.4 - Prove that if {v1, v2} is linearly independent and...Ch. 4.5 - Use the method of Example 3 to show that the...Ch. 4.5 - Use the method of Example 3 to show that the...Ch. 4.5 - Show that the following polynomials form a basis...Ch. 4.5 - Prob. 5ECh. 4.5 - Show that the following matrices form a basis for...Ch. 4.5 - In each part, show that the set of vectors is not...Ch. 4.5 - Show that the following vectors do not form a...Ch. 4.5 - Show that the following matrices do not form a...Ch. 4.5 - Find the coordinate vector of w relative to the...Ch. 4.5 - Find the coordinate vector of v relative to the...Ch. 4.5 - Find the coordinate vector of p relative to the...Ch. 4.5 - In Exercises 1516, first show that the set S =...Ch. 4.5 - In Exercises 1718, first show that the set S =...Ch. 4.5 - In words, explain why the sets of vectors in parts...Ch. 4.5 - In any vector space a set that contains the zero...Ch. 4.5 - The accompanying figure shows a rectangular...Ch. 4.5 - The accompanying figure shows a rectangular...Ch. 4.5 - Consider the coordinate vectors...Ch. 4.5 - The basis that we gave for M22 in Example 4...Ch. 4.5 - Prove that if V is a subspace of a vector space W...Ch. 4.5 - In parts (a)(e) determine whether the statement is...Ch. 4.5 - In parts (a)(e) determine whether the statement is...Ch. 4.5 - In parts (a)(e) determine whether the statement is...Ch. 4.5 - In parts (a)(e) determine whether the statement is...Ch. 4.5 - In parts (a)(e) determine whether the statement is...Ch. 4.6 - In Exercises 16, find a basis for the solution...Ch. 4.6 - In Exercises 16, find a basis for the solution...Ch. 4.6 - In Exercises 16, find a basis for the solution...Ch. 4.6 - In each part, find a basis for the given subspace...Ch. 4.6 - Find the dimension of each of the following vector...Ch. 4.6 - a. Show that the set W of all polynomials in P2...Ch. 4.6 - Find a standard basis vector for R3 that can be...Ch. 4.6 - Let {v1, v2, v3} be a basis for a vector space V....Ch. 4.6 - The vectors v1 = (1, 0, 0, 0) and v2 = (1, 1, 0,...Ch. 4.6 - Find a basis for the subspace of R4 that is...Ch. 4.6 - Let S be a basis for an n-dimensional vector space...Ch. 4.6 - Let S = {v1, v2,, vr} be a nonempty set of vectors...Ch. 4.6 - State the two parts of Theorem 4.6.2 in...Ch. 4.6 - In each part, let S be the standard basis for P2....Ch. 4.6 - In parts (a)(k) determine whether the statement is...Ch. 4.6 - In parts (a)(k) determine whether the statement is...Ch. 4.6 - In parts (a)(k) determine whether the statement is...Ch. 4.6 - In parts (a)(k) determine whether the statement is...Ch. 4.6 - In parts (a)(k) determine whether the statement is...Ch. 4.8 - In Exercises 34, determine whether b is in the...Ch. 4.8 - In Exercises 78, find the vector form of the...Ch. 4.8 - In Exercises 910, find bases for the null space...Ch. 4.8 - In Exercises 1112, a matrix in row echelon form is...Ch. 4.8 - In Exercises 1415, find a basis for the subspace...
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Similar questions
- 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 methodsarrow_forwardPlane 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)arrow_forwardshow 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 = 45arrow_forward
- Chapter 4 Quiz 2 As always, show your work. 1) FindΘgivencscΘ=1.045. 2) Find Θ given sec Θ = 4.213. 3) Find Θ given cot Θ = 0.579. Solve the following three right triangles. B 21.0 34.6° ca 52.5 4)c 26° 5) A b 6) B 84.0 a 42° barrow_forwardQ1: 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_forward
- Three 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_forwarddent 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_forward
- 5x 2x+y+ 3x + 3y 4 6arrow_forwardCalculați (a-2023×b)²⁰²⁴arrow_forwardA student completed the problem below. Identify whether the student was correct or incorrect. Explain your reasoning. (identification 1 point; explanation 1 point) 4x 3x (x+7)(x+5)(x+7)(x-3) 4x (x-3) (x+7)(x+5) (x03) 3x (x+5) (x+7) (x-3)(x+5) 4x²-12x-3x²-15x (x+7) (x+5) (x-3) 2 × - 27x (x+7)(x+5) (x-3)arrow_forward
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