Let \( \mathbf{u}=\langle 4,-2\rangle \) and \( \mathbf{v}=\langle-3,-5\rangle \). Express \( \mathbf{u}+\mathbf{v} \) in the form \( \langle a, b\rangle \). \( \mathbf{u + v}=\mathbf{n} \) (Simplify your answers.)

To find \( \mathbf{u} + \mathbf{v} \), we simply add the corresponding components of the vectors \( \mathbf{u} \) and \( \mathbf{v} \). Given: \[ \mathbf{u} = \langle 4, -2 \rangle \quad \text{and} \quad \mathbf{v} = \langle -3, -5 \rangle \] Calculating \( \mathbf{u} + \mathbf{v} \): \[ \mathbf{u} + \mathbf{v} = \langle 4 + (-3), -2 + (-5) \rangle = \langle 4 - 3, -2 - 5 \rangle = \langle 1, -7 \rangle \] Thus, \[ \mathbf{u + v} = \mathbf{n} = \langle 1, -7 \rangle \]