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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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.]
Suppose a₁, a2, a3, a4, and a5 are vectors in R ³, A = (a₁ | 8₂ | a3 | a | a5), and a. Select all of the true statements (there may be more than one correct answer). 3 A. span{a₁, a2, a3, a4} = R ³ 3 | B. span{a₁, a2, a3} = R³ C. {a₁, a₂} is a linearly independent set D. {a₁, a₂ } is a basis for R ³ 3 | E. {a₁, A₂, A3, A4} is a basis for R F. {a₁, a₂, a3} is a linearly independent set G. {a₁, a₂, a3 } is a basis for R ³ 3 3 H. span{a₁, a₂} R ³ = rref(A) = |I. {A₁, A₂, A3, A4} is a linearly independent set 9 1 0 0 1 0 0 -4 0 -1 1 1 NL 2 2
1) Let a = 1 and b= 0 0 1 be two vectors. -1 What is |a|2|b|2+|ab|²?
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.
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
a +c a) Let S = {[a – b] |a, b € R}. Find three vectors in R3 so that each vector in S b – a can be written as a linear combination of the three vectors. Are these vectors linearly independent? Justify your answer. 1 2 -2 1 1 -1 b) Let A = [1 "J. Determine whether the rows of A are linearly 2 4 -5 4 -2 -4 4 -1 independent. Evaluate | - 242| and |3A-1|.
2. Show that if x and y are two vectors, then 3. two n-vectors then prove that
Suppose a1, a2, a3, a4, and ag are vectors in R°, A = (a1 | a2 | as | a4 | a5), and -5 4 rref(A) = 0 1 0 0 0 1 -2 2 1 1 a. Select all of the true statements (there may be more than one correct answer). OA. span{a1, a2, ag} = R OB. {a1, a2, a3} is a basis for R Oc. {a1, a2, a3, a4} is a basis for R3 OD. span{a1, a2, ag, a4} = R³ OE. {a1, a2, a3, a4} is a linearly independent set OF. {a1, a2, az} is a linearly independent set OG. {a1, az} is a linearly independent set OH. {a1, a2} is a basis for R3 OI. span{a1, a2} b. If possible, write a, as a linear combination of a, a2, and ag; otherwise, enter DNE. a4 = c. The dimension of the column space of A is and the column space of A is a subspace of d. Find a basis for the column space of of A. If necessary, enter a1 for a,, etc., or enter coordinate vectors of the form or . Enter your answer as a comma separated list of vectors. A basis for the column space of A is { e. The dimension of the null space of A is and the null space of A is a…
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.
Could a set of three vectors in R* span all of R*? Explain. What about n vectors in R™ when n is less than m? Could a set of three vectors in R* span all of R*? Explain. Choose the correct answer below. A. No. There is no way for any number of vectors in R* to span all of R. B. Yes. Any number of vectors in R* will span all of Rª Yes. A set of n vectors in R™ can span R™ when n

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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?