Help.Especailly (C). That a2 is in W, Please how can the vector a2 can be written as the linear combination. 1.3.3310 -20 2Denote the columns of A by a,, a,, az, and let W = Span (a,, a2, a3-Let A =-4and b=- 2-2 6616a. Is b in fa1, a2, az}? How many vectors are in fa1, az2, az}?b. Is b in W? How many vectors are in W?c. Show that a, is in W. [Hint: Row operations are unnecessary.]a. Is b in fa,, az, az}? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.O A. Yes, bis in fa1, a2, az} since, although b is not equal to a,, a2, or az, it can be expressed as a linear combination of them. In particular, b = ( )a, + (Da2 + ( Da3.(Simplify your answers.)O B. Yes, b is in fa1, a2, az} since b = a(Type a whole number.)O C. No, b is not in fa1, az, az since it cannot be generated by a linear combination of a,, a,, and azO D. No, b is not in fa,, az, az) since b is not equal to a,, a2, or az

Answered: Image /qna-images/answer/b1e525ba-3634-4a28-abd1-64f9a1cc64c7.jpg

10 -2 -2 -2 Denote the columns of A by a,, a2, a3, and let W = Span (a,, a2, az}. - 16 Let A = 0 2 -4 and b = -2 6 6. a. Is b in (a,, a2, az}? How many vectors are in (a,, 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.]

10 -2 -2 -2 Denote the columns of A by a,, a2, a3, and let W = Span (a,, a2, az}. - 16 Let A = 0 2 -4 and b = -2 6 6. a. Is b in (a,, a2, az}? How many vectors are in (a,, 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.]

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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Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

Help.

Especailly (C). That a2 is in W, Please how can the vector a2 can be written as the linear combination.

1.3.33
10 -2
0 2
Denote the columns of A by a,, a,, az, and let W = Span (a,, a2, a3-
Let A =
-4
and b=
- 2
-2 6
6
16
a. Is b in fa1, a2, az}? How many vectors are in fa1, az2, az}?
b. Is b in W? How many vectors are in W?
c. Show that a, is in W. [Hint: Row operations are unnecessary.]
a. Is b in fa,, az, az}? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
O A. Yes, bis in fa1, a2, az} since, although b is not equal to a,, a2, or az, it can be expressed as a linear combination of them. In particular, b = ( )a, + (Da2 + ( Da3.
(Simplify your answers.)
O B. Yes, b is in fa1, a2, az} since b = a
(Type a whole number.)
O C. No, b is not in fa1, az, az since it cannot be generated by a linear combination of a,, a,, and az
O D. No, b is not in fa,, az, az) since b is not equal to a,, a2, or az

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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