To see why this is so, draw two points h and i in the xy-plane. Now use the Pythagorean theorem for right triangles (a2 + b2 = c2) to find the distance between the two points h and i. Find the Euclidean distance between the points h =(3,5) and i =(7,10).
Find the Euclidean length of the 2-D vector x = (1,4). [This is also equivalent to asking: find the Euclidean distance between the point h = (1,4) and i = (0,0).] Find the length of the 2-D vector y = (8,5).
You verified that this formula was correct by using a ruler and creating a 3-D plot system in the assembler section of the lab. Can you prove this by applying the Pythagorean theorem twice? Hint: First prove that the distance in the flat 2-D surface is (x12+x22)1/2.
Find the length of the 5-D vector x=(1 3 4 0 9) T.
Compute the nearest rank-3 matrix A3, and compare it to the A3 represented on page 7.
|.98 × 10-5|
|.33 × 10-5|
|.72 × 10-6|
|.19 × 10-6|