10:01 CThe column space of A is the set of all vectors that are linear combinations of thecolumns of A-2 13 and u=4-21. Let A =-2 -57and v--1-13-8a) Determine if u is in Nul (A). Could u be in Col A?Add a caption...> Status (Custom) 10:01 C1. Determine whether vis in the column space or null space of A=Add a caption...> Status (Custom)

Given matrix A=24-21-2-57337-86 and u=3-2-10 and v=3-13 Remarks If AX=0then x in Null(A)

Answered: The column space of A is the set of all…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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If A = [a1, a2, a3] has as columns the three vectors a1, a2, and a3. What is y = Ax,where x is a vector with three components, x1, x2, x3? Is y in the column spaceof A?
Let A = 10-3 02-2 - 4 4 2 and b = - 1 - 2 6 Denote the columns of A by a₁, a₂, a3, and let W = Span {a₁, a2, ª3}. a. Is b in {a₁, a₂, a3}? How many vectors are in {a₁, a2, a3}? b. Is b in W? How many vectors are in W? c. Show that a, is in W. [Hint: Row operations are unnecessary.]
If u, v, w and z are vectors in R", which of the following expressions does not make mathematical sense? A. They are all valid expressions. B. (u + v). w (u.v)(w.z) ||u|| C. (u.v)||w|| Z U.V ||w||(z.w) Reset Selection E.
а +с] a) Let S Find three vectors in R3 so that each vector a - b - a in S can be written as a linear combination of the three vectors. Are these vectors linearly independent? Justify your answer. 1 -2 1 1 1 -1 Let A = 2 Determine whether the rows of A are 4 4 -5 [-2 -4 4 -1 linearly independent. Evaluate | – 2A²| and13A¬1|.
6. Let ū, ī, and w be vectors. Explain why any linear combination of i and i is also a linear combination of ū, ī, and w.
Let A = b 6 3 -6 3 0 4 3 1 and b = a₁+ a3= a. Is b in {a₁, a2, a3}? [Select an answer b. How many vectors are in {a₁, a2, a3}? (Enter o for infinitely many.) c. Is b in Span{a₁, a2, a3}? Select an answer d. If b is in Span{a₁, a2, a3}, write b as a linear combination of a₁, a2, a3. Don't write anything if b is not in Span{a₁, a2, a3}. a₂+ -27 -27 a₂+ a3 e. How many vectors are in Span{a₁, a2, a3}? (Enter ∞o for infinitely many.) . Denote the columns of A by a₁1, a2, a3. f. Show that az is in Span{a1, a2, a3} by writing a3 as a linear combination of a1, a2, a3. a₁+ a3
Consider the following vectors: 3 9. 6 -2 -5 -6 a = 8 1 1 9. For each of the following vectors, determine whether it is in span{a, 6. c}. If so, express it as a linear combination using a, b, and c as the names of the vectors above. 9. V1 = 9. -7 -15 13 -8 -17 18 -10 16
Let ||v|| = 3. Which of the following vectors is a possible value of ~v?
Let A = 10 - 6 03 - 4 and b = -39 2 11 - 1 - 28 Denote the columns of A by a₁, a2, a3, and let W = Span {a₁, a₂, a3}. a. Is b in {a₁, a₂, a3}? How many vectors are in {a₁, a2, a3}? b. Is b in W? How many vectors are in W? c. Show that a2 is in W. [Hint: Row operations are unnecessary.] a. Is b in {a₁, a₂, a3}? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. Yes, b is in {a₁, a2, a3} since b=a (Type a whole number.) B. No, b is not in {a₁, a2, a3} since b is not equal to a₁, a2, or a3. C. Yes, b is in (a₁, a2, a3} since, although b is not equal to a₁, a₂, or a3, it can be expressed as a linear combination of them. In particular, b = (Simplify your answers.) аз. D. No, b is not in {a₁, a2, a3} since it cannot be generated by a linear combination of a₁, a2, and ) a₁ + a₂ + ( ) a3.
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a. Write the vector (-4,-8, 6) as a linear combination of a₁ (1, -3, -2), a₂ = (-5,–2,5) and ẩ3 = (−1,2,3). Express your answer in terms of the named vectors. Your answer should be in the form 4ả₁ + 5ả₂ + 6ẩ3, which would be entered as 4a1 + 5a2 + 6a3. (-4,-8, 6) = -3a1+a2+2a3 b. Represent the vector (-4,-8,6) in terms of the ordered basis = {(1, −3,−2), (-5, -2,5),(-1,2,3)}. Your answer should be a vector of the general form . [(-4,-8,6)] =
Let the following vectors be in R³ a = (1,3,-1) b = (-2,1,3) c = (3,2,1) d= (1, -1,2) * 12- Find the distance of the following vectors: (a – d)² + (2c - b) = a² * (b-d+c) =

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The column space of A is the set of all vectors that are linear combinations of the columns of A. 3 -2 1] 1. Let A =|-2 -5 7 3 and u -8 6] 4 -2 and v= 1 3 7 a) Determine if u is in Nul (A). Could u be in Col A?