0 -40 3-2 6by a1, a2, az and W1.4. Let Aand b=Denote the columns of Aspan{a, az, a3}.(a) Is b in W? How many vectors are in W?(b) Is b in the set {a, a2, a3}? How many vectors are in {a1, a2, a3}?

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Answered: 0 -4 0 3 -2 6 by a1, a2, az and W 1. 4.…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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
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.
1. For the cross product between vectors a=[h, -1, 8] and b=[k, 5, 7] to be axb= [-47, -5, 17], what values must h and k be?
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
1 0 -4 3 -2| and 6 Let A Denote the columns of A by d1, å2, åz , and let W = Span{ă1, ă2, ā3}. -2 6 3 A. Is in {ã1, ă2, åz} ? How many vectors are in {ã1, a2, dz}? B. Is 6 in W? How many vectors are in W? C. Show that a is in W. [Hint: Row operations are unnecessary.]
2. Show that if x and y are two vectors, then 3. two n-vectors then prove that
The vector y is a numerical vector. Which ONE of the following best describes what the R code below will calculate? sum(!is.na(y)) A logical vector of the same length as the vector y, which takes the value TRUE for values in y which are NOT missing and FALSE for values in y which ARE missing. Replaces each value in y with TRUE if it is not missing and FALSE if it is missing The number of non-missing values in the vector y. The number of missing values in the vector y. The propostion of non-missing values in the vector y.
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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0 -4 0 3 -2 6 by a1, a2, az and W 1. 4. Let A and b= Denote the columns of A span{a, az, a3}. (a) Is b in W? How many vectors are in W? (b) Is b in the set {a, a2, a3}? How many vectors are in {a1, a2, a3}?