Let a, a2,... , ak ER, let b,b, ..., bk E Rm, and let C, C,...

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Let a₁, a2,... , ak ER", let b₁,b₂, ..., bk E Rm, and let C₁, C₂, ..., Ck E Rn+m [B] bi C₁ = for each i = 1, 2, ..., k. (a) If a₁, a2, follow C₁, C2, (b) If a₁, a₂, follow C1, C₂, be defined by ak is linearly independent, and we make no assumptions about b₁,b₂, ..., bk, does it ,Ck is linearly independent? Why or why not? ak is linearly dependent, and we make no assumptions about b₁,b2, ..., bk, does it Ck is linearly dependent? Why or why not? Let a₁, a2,... , ak ER", let b₁,b₂, ..., bk E Rm, and let C₁, C₂, ..., Ck E Rn+m [B] bi C₁ = for each i = 1, 2, ..., k. (a) If a₁, a2, follow C₁, C2, (b) If a₁, a₂, follow C1, C₂, be defined by ak is linearly independent, and we make no assumptions about b₁,b₂, ..., bk, does it ,Ck is linearly independent? Why or why not? ak is linearly dependent, and we make no assumptions about b₁,b2, ..., bk, does it Ck is linearly dependent? Why or why not?