Express the indicated vector w as a linear combination of the given vectors v, and v, if this is possible. If not, show that it is impossible. 7 4 -4 v, = 3 8 w = 8 7 Select the correct answer below, and fill in the answer box(es) to complete your choice. O A. It is possible to express the vector w in terms of v, and v,, as w = V2. (Type integers or fractions.) O B. It is impossible to express the vector w in terms of v, and v2, because an echelon form of the augmented matrix [v, v2 w], E= is inconsistent. (Type an integer or simplified fraction for each matrix element.) shows that the system

Express the indicated vector w as a linear combination of the given vectors v, and v, if this is possible. If not, show that it is impossible. 7 4 -4 v, = 3 8 w = 8 7 Select the correct answer below, and fill in the answer box(es) to complete your choice. O A. It is possible to express the vector w in terms of v, and v,, as w = V2. (Type integers or fractions.) O B. It is impossible to express the vector w in terms of v, and v2, because an echelon form of the augmented matrix [v, v2 w], E= is inconsistent. (Type an integer or simplified fraction for each matrix element.) shows that the system

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

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.

Question

Express the indicated vector w as a linear combination of the given vectors v, and v, if this is possible. If not, show that it is impossible.
7
1
- 4
-8
w =
V1 =
Vっ=
3
6
9
8
7
Select the correct answer below, and fill in the answer box(es) to complete your choice.
O A. It is possible to express the vector w in terms of v, and v,, as w =
V2-
(Type integers or fractions.)
O B. It is impossible to express the vector w in terms of v, and v,, because an echelon form of the augmented matrix [v, v, w], E =
shows that the system
is inconsistent.
(Type an integer or simplified fraction for each matrix element.)

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