Answered: Show that dim(W1) + dim(W2) – dim(W1n…

Show that dim(W1) + dim(W2) – dim(W1n W2) = dim(W1 + W2), where W1 + W½ just denotes the span of W1 U W2 in V. (Hint: Apply the rank nullity theorem to the natural map W1 O W2 → V .)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.2: Vector Spaces

Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...

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Question

Let W1 and W2 be two subspaces of a finite dimensional vector space V over a field F.

Show that
dim(W1) + dim(W2) – dim(W1n W2) = dim(W1 + W2),
where W1 + W½ just denotes the span of W1 U W2 in V. (Hint: Apply the rank nullity theorem to the
natural map W1 O W2 → V .)

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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