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Math / Linear Algebra: A Geometric Approach 2 / Chapter 3.4 / Problem 21

Linear Algebra: A Geometric Approach | 2nd Edition | ISBN: 9781429215213 | Authors: Ted Shifrin, Malcolm Adams

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Let U and V be subspaces of Rn. Prove that dim(U + V ) = dim U + dim V dim(U V ). (Hint

Chapter 3, Problem 21

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QUESTION:

Let U and V be subspaces of Rn. Prove that dim(U + V ) = dim U + dim V dim(U V ). (Hint: This is a generalization of Exercise 20. Start with a basis for U V , and use Exercise 17.)

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QUESTION:

Let U and V be subspaces of Rn. Prove that dim(U + V ) = dim U + dim V dim(U V ). (Hint: This is a generalization of Exercise 20. Start with a basis for U V , and use Exercise 17.)

ANSWER:

Step 1 of 3

It is given that, and be subspaces of .

Here we need to prove that, .

Let be a subspace of and be a basis for .

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