Adding and Scaling Vectors in N Dimensions Worksheet with Answer Key

What's on the worksheet

1. Let u = (3, -1, 0, 4, -2, 5), v = (-2, 6, 1, -3, 0, 4) and w = (1, 0, -5, 2, 7, -1) in R^6.
   \mathbf{u} + \mathbf{v} + \mathbf{w}2\mathbf{v} - 3\mathbf{w}\mathbf{u} - (\mathbf{v} - \mathbf{w})\dfrac{1}{2}(\mathbf{u} + \mathbf{v}) - \mathbf{w}
2. Solve 3x + a = b - 2x for x in R^4, where a = (-1, -6, 7, 6) and b = (9, 19, 12, -9).
3. Use the definition of equal vectors.
4. Find the vectors x and y in R^4 with x + 2y = a and x - y = b, where a = (10, 2, 5, 0) and b = (1, -7, -4, -6).
5. Vectors u, v and x in R^n satisfy 3(\mathbf{x} - 2\mathbf{u}) + 2\mathbf{v} = 5\mathbf{x} - (\mathbf{u} - 4\mathbf{v}).
6. The points p = (7, -4, 1, -6), q = (4, 3, -1, 6) and r = (-2, 7, 3, 0) of R^4 are the corners of a triangle.
7. Let u and v be vectors in R^n and c a scalar.