Let T: R³ R³ be the linear transformation defined by 1. Find the kernel of T where: a = B={ 2. Find a basis for N(T), the kernel of T B2={ 1 where: a = X-Z 3. What is the nullity of T? 1 y +z B={ 0 5. Find the range of T 4. Find an orthonormal basis N(T), the kernel of T b= -1 B={ 7. What is the rank of T? } b= } C= 6. Find a basis for the range of T (Use integer components). 6. Find an orthonormal basis for the range of T. c= 1 ETEI d=1 18 } } T(ED) - {1] N(T) = R(T) = -(0)₁ [6x - 4y - 10z] x-z -2x+y+3z_ : ax + bz = 0; cy+dz = 0 y2 ayı + by2 + cy3 = 0
Let T: R³ R³ be the linear transformation defined by 1. Find the kernel of T where: a = B={ 2. Find a basis for N(T), the kernel of T B2={ 1 where: a = X-Z 3. What is the nullity of T? 1 y +z B={ 0 5. Find the range of T 4. Find an orthonormal basis N(T), the kernel of T b= -1 B={ 7. What is the rank of T? } b= } C= 6. Find a basis for the range of T (Use integer components). 6. Find an orthonormal basis for the range of T. c= 1 ETEI d=1 18 } } T(ED) - {1] N(T) = R(T) = -(0)₁ [6x - 4y - 10z] x-z -2x+y+3z_ : ax + bz = 0; cy+dz = 0 y2 ayı + by2 + cy3 = 0
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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![Let T: R³ R³ be the linear transformation defined by
1. Find the kernel of T
where: a =
B={
2. Find a basis for N(T), the kernel of T
B2={
1
where: a =
X-Z
3. What is the nullity of T? 1
y +z
B={
0
5. Find the range of T
4. Find an orthonormal basis N(T), the kernel of T
b= -1
B={
7. What is the rank of T?
}
b=
}
C=
6. Find a basis for the range of T (Use integer components).
6. Find an orthonormal basis for the range of T.
c=
1
ETEI
d=1
18
}
}
T(ED) -
{1]
N(T) =
R(T) =
-(0)₁
[6x - 4y - 10z]
x-z
-2x+y+3z_
: ax + bz = 0; cy+dz = 0
y2 ayı + by2 + cy3 = 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a4eeb32-1652-4622-80f9-de25f0a55277%2Fdc59102e-6eaa-4741-86ba-b420d603aba6%2Fkdz9f3f_processed.png&w=3840&q=75)
Transcribed Image Text:Let T: R³ R³ be the linear transformation defined by
1. Find the kernel of T
where: a =
B={
2. Find a basis for N(T), the kernel of T
B2={
1
where: a =
X-Z
3. What is the nullity of T? 1
y +z
B={
0
5. Find the range of T
4. Find an orthonormal basis N(T), the kernel of T
b= -1
B={
7. What is the rank of T?
}
b=
}
C=
6. Find a basis for the range of T (Use integer components).
6. Find an orthonormal basis for the range of T.
c=
1
ETEI
d=1
18
}
}
T(ED) -
{1]
N(T) =
R(T) =
-(0)₁
[6x - 4y - 10z]
x-z
-2x+y+3z_
: ax + bz = 0; cy+dz = 0
y2 ayı + by2 + cy3 = 0
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