2. Let $\mathbf{v}=\langle 2,-1\rangle$ and $\mathbf{w}=\langle 3,4\rangle$. Find each expression. a) $\|\mathbf{w}\|=$ b) $\|3 \mathbf{w}-\mathbf{v}\|=$

Step 1 ：Given vectors \(\mathbf{v}=\langle 2,-1\rangle\) and \(\mathbf{w}=\langle 3,4\rangle\)

Step 2 ：We are asked to find the magnitude of \(\mathbf{w}\) and the magnitude of the vector resulting from the operation \(3 \mathbf{w}-\mathbf{v}\)

Step 3 ：The magnitude of a vector \(\mathbf{v}=\langle x,y\rangle\) in 2D space is given by the formula \(\|\mathbf{v}\| = \sqrt{x^2+y^2}\)

Step 4 ：For part a), we calculate \(\|\mathbf{w}\| = \sqrt{3^2+4^2}\)

Step 5 ：For part b), we first perform the vector operation \(3 \mathbf{w}-\mathbf{v}\), which results in a new vector \(\langle 7,13 \rangle\)

Step 6 ：Then, we calculate the magnitude of this new vector using the same formula \(\|3 \mathbf{w}-\mathbf{v}\| = \sqrt{7^2+13^2}\)

Step 7 ：Final Answer: a) \(\|\mathbf{w}\| = \boxed{5.0}\) b) \(\|3 \mathbf{w}-\mathbf{v}\| = \boxed{14.7648230602334}\)