Answer to Question #222898 in Linear Algebra for Shaikh

Question #222898

if w is subspace of a vector space V over field F such that dim v=5 and dim w=2 then dim A(w) =

Expert's answer

$\text{Since w is a subspace of v, we have that,}\\dim(w)+dim(A(w))=dim(v) \\\text{$dim(w) = 5-2=3$}$

Learn more about our help with Assignments: Linear Algebra

Comments

No comments. Be the first!

Leave a comment

Related Questions

1. Given a number 𝑑 = 𝑑𝑒𝑡(𝐴1, ⋯ , 𝐴𝑛 ), find 𝑑𝑒𝑡(𝐴𝑛, ⋯ , 𝐴1
2. Suppose 𝑋 is a matrix such that 𝑋 + 𝑋 2 = −𝐼�
3. Given a number 𝑑 = 𝑑𝑒𝑡(𝐴1, ⋯ , 𝐴𝑛 ), find 𝑑𝑒𝑡(𝐴𝑛, ⋯ , 𝐴1
4. Express V= 3t² + 7t + -4 as a linear combination of the polynomialsP1= t² + 2t + 3P2= 2t² + 3t +
5. Determine whether the vectors are linearly dependent or independent (1,2,1),(-1,0,1) and (2,-1,4)
6. Let f:R2→R2 be defined by f(x,y)=(-y,-x)i) show that f is linearii)Determine a basis for the kern
7. Construct an orthonormal basis for the subspace of R3 spanned by the vectors (1,-1,1)and (2,0,4)