Problem 9 Suppose $\mathbf{u}=(3,2)$ and... [FREE SOLUTION]

Sheldon Axler

$Math Studyset 91影视 Explanations$ Math

1 Edition

Chapter 6: Problem 9

Suppose $\mathbf{u}=(3,2)$ and $\mathbf{v}=(4,5)$. Compute $\mathbf{u} \cdot \mathbf{v}$.

Expert verified

The dot product of $\mathbf{u}=(3,2)$ and $\mathbf{v}=(4,5)$ is equal to $\mathbf{u} \cdot \mathbf{v} = 22$.

First, identify the components of both vectors. For $\mathbf{u}$, we have $u_{1}=3$ and $u_{2}=2$. For $\mathbf{v}$, we have $v_{1}=4$ and $v_{2}=5$.

Now, we will multiply the corresponding components of both vectors. We have: - $u_{1}v_{1} = 3 \times 4 = 12$, - $u_{2}v_{2} = 2 \times 5 = 10$.

Finally, add the results of the multiplication to find the dot product: $\mathbf{u} \cdot \mathbf{v} = u_{1}v_{1} + u_{2}v_{2} = 12 + 10 = 22$.

Thus, the dot product of $\mathbf{u}=(3,2)$ and $\mathbf{v}=(4,5)$ is equal to $\mathbf{u} \cdot \mathbf{v} = 22$.

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