Linear algebra: please solve q6 correctly and handwritten
Transcribed Image Text:2. Define T: R² → R² by T(x) = Ax, where
-[₁
Find each of the following.
a) T
T ([²])
*¹([²]).
2
c) T
3. Let T: R³
fined by
A =
x1
1 -1
3
-3
b) T
1
(³)
"T([:))
d)
→ R2 be the linear transformation de-
r
2x 4r. 1
4. Let T: R² →→ R2 be the function defined in Exer-
cise 1. Find x in R2 such that T(x) = b, where
2
»-[ -3].
b =
5. Let T: R² → R2 be the function given in Exer-
cise 1. Show that for each b in R2, there is an x in
R2 such that T(x) = b.
6. Let T be the linear transformation given in Exer-
cise 2. Find x in R2 such that T(x) = b, where
b=
-2
6
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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![2. Define T: R² → R² by T(x) = Ax, where
-[₁
Find each of the following.
a) T
T ([²])
*¹([²]).
2
c) T
3. Let T: R³
fined by
A =
x1
1 -1
3
-3
b) T
1
(³)
"T([:))
d)
→ R2 be the linear transformation de-
r
2x 4r. 1
4. Let T: R² →→ R2 be the function defined in Exer-
cise 1. Find x in R2 such that T(x) = b, where
2
»-[ -3].
b =
5. Let T: R² → R2 be the function given in Exer-
cise 1. Show that for each b in R2, there is an x in
R2 such that T(x) = b.
6. Let T be the linear transformation given in Exer-
cise 2. Find x in R2 such that T(x) = b, where
b=
-2
6](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F282e5c7f-f36f-41bc-95a9-c56962ce4076%2F677967b2-541f-4fa2-8bef-2fdfaabcf45f%2Fy9u3n8_processed.jpeg&w=3840&q=75)
