Questions: In Exercises 15-20, explain why S is not a basis for R^3. 17. S=(7,0,3),(8,-4,1)

Transcript text: In Exercises 15-20, explain why $S$ is not a basis for $R^{3}$. 17. $S=\{(7,0,3),(8,-4,1)\}$

Solution

Step 1: Consider the dimension of R³

A basis for R³ must contain 3 linearly independent vectors.

Step 2: Count the number of vectors in S

The set S contains only two vectors.

Step 3: Determine if S is a basis for R³

Since S contains only two vectors, S cannot span R³ and therefore cannot be a basis for R³.

S is not a basis for R³ because it only contains two vectors, and a basis for R³ must contain three linearly independent vectors.

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