4) Let V = M2x2 (C) with standard basis B = (m₁, m2, m3, m4) and let T : V → (a) (b) (c) T((& $)) = a-d b + c d) V be the map Write down a basis for ^²(V), A³(V) and ^^(V) Find the matrix for ^³(T) : ^³(V) → ^³(V) (hint: it will be a 4×4 matrix) Find the determinant of T

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.1: Orthogonality In Rn
Problem 34EQ
icon
Related questions
Question
100%
4) Let V = M2×2 (C) with standard basis B = (m₁, m2, m3, m4) and let T : V → V be the map
d
-
¹ (( & d)) = ( 8 = & d)
b + c
Write down a basis for ^²(V), ^³(V) and ^^(V)
Find the matrix for ^³(T) : ^³(V) → ^³(V) (hint: it will be a 4×4 matrix)
Find the determinant of T
(a)
(b)
(c)
Transcribed Image Text:4) Let V = M2×2 (C) with standard basis B = (m₁, m2, m3, m4) and let T : V → V be the map d - ¹ (( & d)) = ( 8 = & d) b + c Write down a basis for ^²(V), ^³(V) and ^^(V) Find the matrix for ^³(T) : ^³(V) → ^³(V) (hint: it will be a 4×4 matrix) Find the determinant of T (a) (b) (c)
Expert Solution
steps

Step by step

Solved in 4 steps with 4 images

Blurred answer
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage