In: Advanced Math
Let w,v1,...,vp ∈ Rn and suppose that w ∈ Span{v1,...,vp}. Show that Span{w,v1,...,vp} = Span{v1,...,vp}.
Let v1,...,vp,w1,...,wq ∈ Rm. Is the following statement True or False?
“If {v1, . . . , vp} is linearly dependent then {v1,...,vp,w1,...,wq}
is linearly dependent.”
If you answer True, provide a complete proof; if you answer False,
provide a counter-example. Linear Algebra. Please show both!