Finding coordinates of the projection.

Learning Goal: I’m working on a linear algebra multi-part question and need an explanation and answer to help me learn.

1. Consider the point (2,13). Project this point onto the line y = 5x. This projection will have two coordinates in 2-dimensional space. What is the x-coordinate of this projection? (It would be best not to round your answer. But if you do, don’t round to less than four decimal places.)

2. Consider the point (2,13). Project this point onto the line y = 5x. This projection will have two coordinates in 2-dimensional space. What is the y-coordinate of this projection? (It would be best not to round your answer. But if you do, don’t round to less than four decimal places.)

3. Consider the point (2,13). Project this point onto the line y = 5x. If you consider this projection to be part of the one-dimensional space y = 5x, it will have just a single coordinate. What is this coordinate? (It would be best not to round your answer. But if you do, don’t round to less than four decimal places.)

4. Project the points (2,13), (5,10), and (8,4) onto the line y = 5x. What is the variance of these projections along this line? (It would be best not to round your answer, but if you do, don’t round to less than four decimal places.)

5. Project the points (2,13), (5,10), and (8,4) onto the x-axis. What is the variance of these projections along the x-axis? (It would be best not to round your answer, but if you do, don’t round to less than four decimal places.)