1 0- 21Let A =0 3and b =Denote the columns of A by a,, a2, a3, and let W = Span (a1, a2, a3}.- 4%3D-4 62a. Is b in fa,, a2, az}? How many vectors are in {a1, a2, az}?|b. Is b in W? How many vectors are in W?c. Show that a, is in W. [Hint: Row operations are unnecessary.]b. Is b in W? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.O A. Yes, b is in W since, although b is not equal to a,, a2, or a3, it can be expressed as a linear combination of them. In particular,Da, +a2 + (b =az(Simplify your answers.)O B. Yes, b is in W sinceb= a(Type a whole number.)O C. No, b is not in W since it cannot be generated by a linear combination of a,, a,,andaz.O D. No, b is not in W since b is not equal to a1, a2, or a3.

Given A=10-203-2-462 and b=152 Column of A denoted by a1, a2, a3 W=spana1,a2,a3

10 -2 Let A = 0 3 -4 and b= 5 . Denote the columns of A by a, , a2, a3, and let W = Span {aq, a2, a3}. -46 2 2 a. Is b in fa,, a2, az}? How many vectors are in {a,, a2, ag}? 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 Let A = 0 3 -4 and b= 5 . Denote the columns of A by a, , a2, a3, and let W = Span {aq, a2, a3}. -46 2 2 a. Is b in fa,, a2, az}? How many vectors are in {a,, a2, ag}? 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

1 0
- 2
1
Let A =
0 3
and b =
Denote the columns of A by a,, a2, a3, and let W = Span (a1, a2, a3}.
- 4
%3D
-4 6
2
a. Is b in fa,, a2, az}? How many vectors are in {a1, a2, az}?
|
b. Is b in W? How many vectors are in W?
c. Show that a, is in W. [Hint: Row operations are unnecessary.]
b. Is b in W? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
O A. Yes, b is in W since, although b is not equal to a,, a2, or a3, it can be expressed as a linear combination of them. In particular,
Da, +
a2 + (
b =
az
(Simplify your answers.)
O B. Yes, b is in W sinceb= a
(Type a whole number.)
O C. No, b is not in W since it cannot be generated by a linear combination of a,, a,,
and
az.
O D. No, b is not in W since b is not equal to a1, a2, or a3.

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