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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...

  1. Let w,v1,...,vp ∈ Rn and suppose that w ∈ Span{v1,...,vp}. Show that Span{w,v1,...,vp} = Span{v1,...,vp}.

  2. 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!

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