(a) Choose all correct statements: Let S be a linearly independent subset of a vector space R4. If the vector v is in R4, and it is not in S, then the set SU {v} must be linearly independent. Let W be a vector space of dimension 4. A spanning set for W must contain at least 4 vectors. The map F: M33 → M33 defined by F(A) = AB + BA³ , where B = (b) Let T: M22 → R² be the linear map defined by T(X) = X() + X² (₂). where M22 is the set of 2 x 2 real matrices. 551 512) 3 1 1/ 252 , is a linear map. for the domain and (i) Suppose that A is the matrix of the transformation T: M22 → R2 with respect to the standard bases, S₁ = {( ) ( ) ( ) ( )} - {6)·()} S₂ = for the codomain. Find the matrix A and enter your answer, using equation editor, in the box below.
(a) Choose all correct statements: Let S be a linearly independent subset of a vector space R4. If the vector v is in R4, and it is not in S, then the set SU {v} must be linearly independent. Let W be a vector space of dimension 4. A spanning set for W must contain at least 4 vectors. The map F: M33 → M33 defined by F(A) = AB + BA³ , where B = (b) Let T: M22 → R² be the linear map defined by T(X) = X() + X² (₂). where M22 is the set of 2 x 2 real matrices. 551 512) 3 1 1/ 252 , is a linear map. for the domain and (i) Suppose that A is the matrix of the transformation T: M22 → R2 with respect to the standard bases, S₁ = {( ) ( ) ( ) ( )} - {6)·()} S₂ = for the codomain. Find the matrix A and enter your answer, using equation editor, in the box below.
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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Plz complete solution with 100% accuracy I vill upvote it is my last post plz complete it.
Transcribed Image Text:(a) Choose all correct statements:
Let S be a linearly independent subset of a vector space R4. If the vector v is in R4, and it is not in S, then the set
SU{v} must be linearly independent.
Let W be a vector space of dimension 4. A spanning set for W must contain at least 4 vectors.
The map F: M33 M33 defined by F(A) = AB + BA³
(b) Let T: M22 → R2 be the linear map defined by
T(X) = X(
where M22 is the set of 2 x 2 real matrices.
b
sin (a)
(i) Suppose that A is the matrix of the transformation T: M22 R2 with respect to the standard bases,
S₁ =
for the domain and
= {( ) ( ) ( ) (9)}
{6).()}*
S₂ =
for the codomain.
Find the matrix A and enter your answer, using equation editor, in the box below.
Ә
əx
ab sin (a)
f
∞ a Ω
and B = {u₁, u₂} for the codomain, where ₁ =
Ə
f
əx
(2) + X² (₁)
where B =
a 52
(ii) Your friend Benedict is interested in the matrix M of T with respect to the bases S₁ for the domain
(²)
·(¹).
Help Benedict by finding the matrix M and giving your answer, using equation editor, in the box below.
and U₂ =
E
G
5 5 1
252
3 1 1
, is a linear map.
G
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