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Let a be an mn matrix, and let u and v be vectors in irn with the property that au = 0 and av = 0. explain why a(u + v) must be the zero vector. then explain why a(cu + dv) = 0 for each pair of scalars c and
d.

Answer :

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[tex]\mathbf{Au}=\mathbf0[/tex]
[tex]\mathbf{Av}=\mathbf0[/tex]

[tex]\implies\mathbf{Au}+\mathbf{Av}=\mathbf0[/tex]
[tex]\implies\mathbf A(\mathbf u+\mathbf v)=\mathbf0[/tex]

Multiplying by scalars [tex]c,d[/tex] won't change this fact.

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