Vector spaces: Vector spaces and linear subspaces
Affine subspaces
In the vector space #\mathbb{R}^4# we consider the linear subspace \[W=\left\{\rv{x,y,z,u}\mid x+ y- z+ u=0\right\}\] and vectors
\[\vec{a} = \rv{ 4 , 4 , 2 , -10 } \phantom{xxx}\text{and}\phantom{xxx}\vec{b} = \rv{ -1 , 4 , 2 , -3 } \]
Are the two affine subspaces #\vec{a}+W# and #\vec{b}+W# equal to each other?
\[\vec{a} = \rv{ 4 , 4 , 2 , -10 } \phantom{xxx}\text{and}\phantom{xxx}\vec{b} = \rv{ -1 , 4 , 2 , -3 } \]
Are the two affine subspaces #\vec{a}+W# and #\vec{b}+W# equal to each other?
Unlock full access
Teacher access
Request a demo account. We will help you get started with our digital learning environment.
Student access
Is your university not a partner?
Get access to our courses via Pass Your Math independent of your university. See pricing and more.
Or visit omptest.org if jou are taking an OMPT exam.
Or visit omptest.org if jou are taking an OMPT exam.