9. Define the terms linear combination, linear dependence and linear independence as applied to vectors. Suppose a,b and c are three vectors in R". Show that: (i) if a,b and c are linearly dependent then there exist scalars a,ß and y, not all zero, such that aa+ßb+yc=0, (ii) if there exist scalars a,ß and y, not all zero, such that aa+Bb+yc=0 then a,b and c are linearly dependent. State the generalisation of this result to the case of k vectors in R". Use the generalisation to prove the following statements: (a) Any set of vectors containing the zero vector is linearly dependent. Any set of more than n vectors in R" is linearly dependent. (b)

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Q: 3. Determine whether the vectors are linearly independent or are linearly dependent in P2. 1+3x+ 3x,…

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Q: Determine whether the following set of vectors are linearly independent

A: Step 1: Step 2: Step 3: Step 4:

Q: 4.) Are vectors Linearly independent? 2 3

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