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(HD)- 3. Find bases for Null(A), Col(A), Row(A), and Null(AT). Use the Rank-Nullity Theorem to verify your work. You may use MATLAB or a calculator for REF computations as long as you reference in your work what tool you used. Theorem 5.1.30 (Rank-Nullity) Let V and W be finite-dimensional vector spaces and let T : V → W be a linear transformation. Then dim V = Rank (T) + Nullity(T).

(HD)- 3. Find bases for Null(A), Col(A), Row(A), and Null(AT). Use the Rank-Nullity Theorem to verify your work. You may use MATLAB or a calculator for REF computations as long as you reference in your work what tool you used. Theorem 5.1.30 (Rank-Nullity) Let V and W be finite-dimensional vector spaces and let T : V → W be a linear transformation. Then dim V = Rank (T) + Nullity(T).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.9: Properties Of Determinants
Problem 12E
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(HD)- 3. Find bases for Null(A), Col(A), Row(A), and Null(AT). Use the Rank-Nullity Theorem to verify your work. You may use MATLAB or a calculator for REF computations as long as you reference in your work what tool you used.
Transcribed Image Text:(HD)- 3. Find bases for Null(A), Col(A), Row(A), and Null(AT). Use the Rank-Nullity Theorem to verify your work. You may use MATLAB or a calculator for REF computations as long as you reference in your work what tool you used.
Theorem 5.1.30 (Rank-Nullity) Let V and W be finite-dimensional vector spaces and let T : V → W be a linear transformation. Then dim V = Rank (T) + Nullity(T).
Transcribed Image Text:Theorem 5.1.30 (Rank-Nullity) Let V and W be finite-dimensional vector spaces and let T : V → W be a linear transformation. Then dim V = Rank (T) + Nullity(T).
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