91Ó°ÊÓ

Write the standard basis for the vector space. $$R^{6}$$

Describe the zero vector (the additive identity) of the vector space. $$C(-\infty, \infty)$$

Write the standard basis for the vector space. $$R^{4}$$

Use a directed line segment to represent the vector $$\mathbf{u}=(2,-4)$$

Use a directed line segment to represent the vector $$\mathbf{v}=(-2,3)$$

You are provided with the coordinate matrix of \(\mathbf{x}\) relative to a (nonstandard) basis \(B\). Find the coordinate vector of \(\mathbf{x}\) relative to the standard basis in \(R^{\prime \prime}\) $$B=\\{(4,0,7,3),(0,5,-1,-1),(-3,4,2,1),(0,1,5,0)\\}$$ $$[\mathbf{x}]_{B}=[-2,3,4,1]^{T}$$

Verify that \(W\) is a subspace of \(V .\) In each case assume that \(V\) has the standard operations. \(W\) is the set of all functions that are differentiable on \([0,1] . V\) is the set of all functions that are continuous on [0,1]

Describe the zero vector (the additive identity) of the vector space. $$M_{22}$$

Explain why \(S\) is not a basis for \(R^{2}\) $$S=\\{(1,2),(1,0),(0,1)\\}$$

Describe the additive inverse of a vector in the vector space. $$R^{4}$$