Question:medium

If $W_1$ and $W_2$ are finite dimensional subspaces of a vector space $V$, then:

Show Hint

This formula is analogous to the Inclusion-Exclusion Principle for sets: $|A \cup B| = |A| + |B| - |A \cap B|$. If $W_1 \cap W_2 = \{0\}$ (direct sum), then $\dim(W_1 \oplus W_2) = \dim(W_1) + \dim(W_2)$.
Updated On: Jul 29, 2026
  • $\dim(W_1 + W_2) = \dim(W_1) + \dim(W_2)$
  • $\dim(W_1 + W_2) = \dim(W_1) + \dim(W_2) + \dim(W_1 \cap W_2)$
  • $\dim(W_1 + W_2) = \dim(W_1) + \dim(W_2) - \dim(W_1 \cap W_2)$
  • $\dim(W_1 + W_2) = \dim(W_1) + \dim(W_2) + \dim(W_1 \cup W_2)$
Show Solution

The Correct Option is C

Solution and Explanation

Was this answer helpful?
0

Top Questions on Vector space

Questions Asked in CUET (PG) exam