19. Let T: R² R³ be a linear transformation such that T(e₁)u₁ and 7 (e₂) = u₂2, where 1 [4] Find each of the following. u₁ a) T ¹([:]) » ¹ ([-²]) b) T 3 c) T 9¹ (²]) 2 and u₂: 2 [1]
19. Let T: R² R³ be a linear transformation such that T(e₁)u₁ and 7 (e₂) = u₂2, where 1 [4] Find each of the following. u₁ a) T ¹([:]) » ¹ ([-²]) b) T 3 c) T 9¹ (²]) 2 and u₂: 2 [1]
19. Let T: R² R³ be a linear transformation such that T(e₁)u₁ and 7 (e₂) = u₂2, where 1 [4] Find each of the following. u₁ a) T ¹([:]) » ¹ ([-²]) b) T 3 c) T 9¹ (²]) 2 and u₂: 2 [1]
Linear algebra: please solve all parts of q19 correctly and handwritten
Transcribed Image Text:19. Let T: R2 R³ be a linear transformation such
that T (e₁)u₁ and 7(e₂) = u₂, where
1
[4]
Find each of the following.
T (1)
¹ ([-²])
2
a) T
b) T
u₁
3
OT ([2])
2
-[1].
0
and u₂ =
20. Let T: R2
R2 be a linear transformation such
that T (v₁) = u₁ and T(v₂) = u₂, where
0
V₁ =
-[8] -[]
V2
--8---8
[2]
=
and u₂ =
3
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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![19. Let T: R2 R³ be a linear transformation such
that T (e₁)u₁ and 7(e₂) = u₂, where
1
[4]
Find each of the following.
T (1)
¹ ([-²])
2
a) T
b) T
u₁
3
OT ([2])
2
-[1].
0
and u₂ =
20. Let T: R2
R2 be a linear transformation such
that T (v₁) = u₁ and T(v₂) = u₂, where
0
V₁ =
-[8] -[]
V2
--8---8
[2]
=
and u₂ =
3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F282e5c7f-f36f-41bc-95a9-c56962ce4076%2F5cd0d671-44be-4b0d-b23f-da294df15720%2F3www2k_processed.jpeg&w=3840&q=75)
