In Exercises 40-45, express the given vector b as a lin- ear combination of v₁ and v2, where v₁ and v₂ are in Eq. (10). 2 7 [²] -[:] 4 40. b = 42. b = [3] 41. b = 43. b = 0 [:] 0
In Exercises 40-45, express the given vector b as a lin- ear combination of v₁ and v2, where v₁ and v₂ are in Eq. (10). 2 7 [²] -[:] 4 40. b = 42. b = [3] 41. b = 43. b = 0 [:] 0
In Exercises 40-45, express the given vector b as a lin- ear combination of v₁ and v2, where v₁ and v₂ are in Eq. (10). 2 7 [²] -[:] 4 40. b = 42. b = [3] 41. b = 43. b = 0 [:] 0
Linear algebra: please solve q41 and 43 correctly and handwritten. Values are also attached
Transcribed Image Text:In Exercises 40-45, express the given vector b as a lin-
ear combination of v₁ and v2, where v₁ and v₂ are in
Eq. (10).
40. b =
2
[²]
7
0
-[:]
4
42. b =
[3]
41. b =
43. b =
0
[:]
Transcribed Image Text:The vectors listed in Eq. (10) are used in several of the
exercises that follow.
2
--8--8--8
-[3].
V2
V1
2
--)--[]
V5
0
3
3
6
----
--0-0-0
U4
2
2
=
4
2
[3]
(10)
Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.
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![In Exercises 40-45, express the given vector b as a lin-
ear combination of v₁ and v2, where v₁ and v₂ are in
Eq. (10).
40. b =
2
[²]
7
0
-[:]
4
42. b =
[3]
41. b =
43. b =
0
[:]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F624dcfab-19f1-4c4b-b3ec-94b9a5b18d08%2F07adc7ff-2523-4f08-a148-82bfb27a8688%2Fycc1orr_processed.jpeg&w=3840&q=75)
![The vectors listed in Eq. (10) are used in several of the
exercises that follow.
2
--8--8--8
-[3].
V2
V1
2
--)--[]
V5
0
3
3
6
----
--0-0-0
U4
2
2
=
4
2
[3]
(10)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F624dcfab-19f1-4c4b-b3ec-94b9a5b18d08%2F07adc7ff-2523-4f08-a148-82bfb27a8688%2Fhiw640e_processed.jpeg&w=3840&q=75)
