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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

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

Advanced Engineering Mathematics
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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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)
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