2. Show thatdim(W1) + dim(W2) – dim(W1 n W2) = dim(W1 + W2),where W1 + W2 just denotes the span of W1U W2 in V. (Hint: Apply the rank nullity theorem to the naturalmap Wi O W2→ V.)

Answered: Image /qna-images/answer/3113f9f7-c7bc-4495-b1b0-e339e73fd739.jpg

Answered: Show that dim(W1) + dim(W2) – dim(W1 n…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.5: The Kernel And Range Of A Linear Transformation

Problem 10EQ

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Show that dim(W1) + dim(W2) – dim(W1 n W2) = dim(W1 + W2), where W1 + W2 just denotes the span of W1 u W2 in V. (Hint: Apply the rank nullity theorem to the natura map Wi O W2 → V.)