Problem 34 In Exercises $21-38,$ let $$... [FREE SOLUTION]

Chapter 7: Problem 34

In Exercises $21-38,$ let $$\mathbf{u}=2 \mathbf{i}-5 \mathbf{j}, \mathbf{v}=-3 \mathbf{i}+7 \mathbf{j}, \text { and } \mathbf{w}=-\mathbf{i}-6 \mathbf{j}$$ Find each specified vector or scalar. $$4 w-3 v$$

Short Answer

Expert verified

The answer is $5\mathbf{i}-45\mathbf{j}$

Step by step solution

- Scalar Multiplication

Perform scalar multiplication for $4 \mathbf{w}$ and $3 \mathbf{v}$:\[4 \mathbf{w}=4(-\mathbf{i}-6 \mathbf{j})=-4 \mathbf{i}-24 \mathbf{j}\] and\[-3 \mathbf{v}=-3(-3 \mathbf{i}+7 \mathbf{j})=9 \mathbf{i}-21 \mathbf{j}\]

- Vector Addition

Add both vectors obtained in Step 1:\[-4 \mathbf{i}-24 \mathbf{j} + 9 \mathbf{i}-21 \mathbf{j} = (9-4)\mathbf{i} +(-21-24)\mathbf{j} = 5\mathbf{i}-45\mathbf{j}\]

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91影视

In Exercises \(21-38,\) let $$\mathbf{u}=2 \mathbf{i}-5 \mathbf{j}, \mathbf{v}=-3 \mathbf{i}+7 \mathbf{j}, \text { and } \mathbf{w}=-\mathbf{i}-6 \mathbf{j}$$ Find each specified vector or scalar. $$4 w-3 v$$

Short Answer

Step by step solution

- Scalar Multiplication

- Vector Addition

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