Let $v = - 8 i + 4 j$ and $w = - i - 3 j$ . Find $5 v - 9 w$ .
$5 v - 9 w = ◻$ (Simplify your answer. Type your answer in terms of $i$ and j.)

Answer

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Answer

Final Answer: The result of the operation $5 v - 9 w$ is $- 49 i - 7 j$ .

Steps

Step 1 ：Let's start by multiplying each vector by their respective scalar. For vector v, we multiply it by 5, and for vector w, we multiply it by -9.

Step 2 ：Doing this, we get: $5 v = 5 (- 8 i + 4 j) = - 40 i + 20 j$ and $- 9 w = - 9 (- i - 3 j) = 9 i + 27 j$ .

Step 3 ：Now, we subtract the two results to get the final vector: $5 v - 9 w = (- 40 i + 20 j) - (9 i + 27 j)$ .

Step 4 ：Simplifying this, we get: $- 40 i + 20 j - 9 i - 27 j = - 49 i - 7 j$ .

Step 5 ：Final Answer: The result of the operation $5 v - 9 w$ is $- 49 i - 7 j$ .