Final answer:
The image of the point (2, 1, 4) under the linear transformation L(x, y, z) = (x + y, 2x, y + 2z) is (3, 4, 9).
Step-by-step explanation:
The student asked to find the image of the point (2, 1, 4) under the linear transformation L(x, y, z) = (x + y, 2x, y + 2z). To find the image, we substitute the original point's coordinates into the transformation equations.
- For the first component: x + y = 2 + 1 = 3
- For the second component: 2x = 2(2) = 4
- For the third component: y + 2z = 1 + 2(4) = 1 + 8 = 9
Therefore, the image of the point (2, 1, 4) under the given linear transformation is (3, 4, 9).