1. The problem asks to sketch the vector field for the function \( \mathbf{F}(x,y) = 2\mathbf{i} - \mathbf{j} \).\n\n2. This vector field assigns the vector \( 2\mathbf{i} - \mathbf{j} \) to every point \( (x,y) \) in the plane.\n\n3. The vector \( 2\mathbf{i} - \mathbf{j} \) means a vector with an x-component of 2 and a y-component of -1.\n\n4. Since this vector is constant (does not depend on \( x \) or \( y \)), the vector field consists of identical vectors pointing right 2 units and down 1 unit at every point.\n\n5. To sketch, draw several vectors of the same length and direction at different points in the plane, making sure they do not intersect.\n\n6. The formula used here is simply the vector field definition: \( \mathbf{F}(x,y) = 2\mathbf{i} - \mathbf{j} = \langle 2, -1 \rangle \).\n\n7. Important rule: constant vector fields have the same vector everywhere, so the field looks uniform.\n\nFinal answer: The vector field \( \mathbf{F}(x,y) = 2\mathbf{i} - \mathbf{j} \) is a uniform field with vectors pointing right 2 units and down 1 unit at every point.