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Let u = 6 - 1 and v= 6 Show that a a -[:] k Let b = k How can it be shown that a vector b is in Span {u, v}? is in Span {u, v} for all a and k. A. Determine if the system containing u, v, and b is consistent. If the system is consistent, then b is in Span {u, v}. B. Determine if the system containing u, v, and b is consistent. If the system is consistent, b might be in Span {u, v}. C. Determine if the system containing u, v, and b is consistent. If the system is consistent, then b is not in Span {u, v}. D. Determine if the system containing u, v, and b is consistent. If the system is inconsistent, then b is in Span {u, v}. Find the augmented matrix [uv b]

Let u = 6 - 1 and v= 6 Show that a a -[:] k Let b = k How can it be shown that a vector b is in Span {u, v}? is in Span {u, v} for all a and k. A. Determine if the system containing u, v, and b is consistent. If the system is consistent, then b is in Span {u, v}. B. Determine if the system containing u, v, and b is consistent. If the system is consistent, b might be in Span {u, v}. C. Determine if the system containing u, v, and b is consistent. If the system is consistent, then b is not in Span {u, v}. D. Determine if the system containing u, v, and b is consistent. If the system is inconsistent, then b is in Span {u, v}. Find the augmented matrix [uv b]

Advanced Engineering Mathematics
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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6 +---- and v= - 1 Let u = 6 Show that a k How can it be shown that a vector b is in Span {u, v}? Let b = is in Span {u, v} for all a and k. A. Determine if the system containing u, v, and b is consistent. If the system is consistent, then b is in Span {u, v}. a A B. Determine if the system containing u, v, and b is consistent. If the system is consistent, b might be in Span {u, v}. C. Determine if the system containing u, v, and b is consistent. If the system is consistent, then b is not in Span {u, v}. D. Determine if the system containing u, v, and b is consistent. If the system is inconsistent, then b is in Span {u, v}. Find the augmented matrix u v b b].
Transcribed Image Text:6 +---- and v= - 1 Let u = 6 Show that a k How can it be shown that a vector b is in Span {u, v}? Let b = is in Span {u, v} for all a and k. A. Determine if the system containing u, v, and b is consistent. If the system is consistent, then b is in Span {u, v}. a A B. Determine if the system containing u, v, and b is consistent. If the system is consistent, b might be in Span {u, v}. C. Determine if the system containing u, v, and b is consistent. If the system is consistent, then b is not in Span {u, v}. D. Determine if the system containing u, v, and b is consistent. If the system is inconsistent, then b is in Span {u, v}. Find the augmented matrix u v b b].
Let A = 1 0 -6 03-5 -59 4 and b = 9 -2. Denote the columns of A by a₁, a2, a3, and let W = Span {a₁, a2, ª3}. - 29 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. No, b is not in (a₁, a2, aç} since b is not equal to a₁, a2, or a3. B. Yes, b is in (a₁, a2, a3} since b = a (Type a whole number.) 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 = (a₁ + a₂ + ([ аз. (Simplify your answers.) D. No, b is not in {a₁, a2, a3} since it cannot be generated by a linear combination of a₁, №₂, and аз.
Transcribed Image Text:Let A = 1 0 -6 03-5 -59 4 and b = 9 -2. Denote the columns of A by a₁, a2, a3, and let W = Span {a₁, a2, ª3}. - 29 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. No, b is not in (a₁, a2, aç} since b is not equal to a₁, a2, or a3. B. Yes, b is in (a₁, a2, a3} since b = a (Type a whole number.) 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 = (a₁ + a₂ + ([ аз. (Simplify your answers.) D. No, b is not in {a₁, a2, a3} since it cannot be generated by a linear combination of a₁, №₂, and аз.
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