Vector and Matrix

Exercise Let u = (1,-5), v = (2, 4 ,1), w = (3, 0, 1, -1, 4), x = (2, -4, 3), y = (-7, 2, 1), z = (1, 2, 0, -3, 4). Compute.

u + v, v + y, y + v, w + z, z + w, x + y + v,

2u, -3v, -w, 0x,

2u + 5v, -2y + 3v, w - 3z, 4x + 2y + v.

Answer

u + v is meaningless
v + y = (2 - 7, 4 + 2, 1 + 1) = (-5, 6, 2)
y + v = (- 7 + 2, 2 + 4, 1 + 1) = (-5, 6, 2)
w + z = (3 + 1, 0 + 2, 1 + 0, - 1 - 3, 4 + 4) = (4, 2, 1, -4, 8)
z + w = (1 + 3, 2 + 0, 0 + 1, - 3 - 1, 4 + 4) = (4, 2, 1, -4, 8)
x + y + v = (2 - 7 + 2, - 4 + 2 + 4, 3 + 1 + 1) = (-3, 2, 5)

2u = (2×1, 2×(-5)) = (2, -10)
-3v = (-3×2, -3×4, -3×1) = (-6, -12, -3)
-w = -(3, 0, 1, -1, 4) = (-3, 0, -1, 1, -4)
0x = (0, 0, 0)

2u + 5v is meaningless
-2y + 3v = -2(-7, 2, 1) + 3(2, 4 ,1) = (-2×(-7) + 3×2, -2×2 + 3×4, -2×1 + 3×1) = (20, 8, 1)
w - 3z = (3, 0, 1, -1, 4) - 3(1, 2, 0, -3, 4) = (3 - 3×1, 0 - 3×2, 1 - 3×0, - 1 - 3×(-3), 4 - 3×4) = (0, -6, 1, 8, -8)
4x + 2y + v = 4(2, -4, 3) + 2(-7, 2, 1) + (2, 4 ,1) = (4×2 + 2×(-7) + 2, 4×(-4) + 2×2 + 4 , 4×3 + 2×1+ 1) = (-4, 8, 15)