Solution to Exercise 3.57.
Great is the power of steady misrepresentation; the history of science shows that fortunately this power does not long endure.
—Charles Darwin (1809–1882)

Exercise 3.57. Find a matrix of the translation that maps the point X(3, 8, 1) to Y(5, 1, 1) and find the image of Z(12, 7, 1). Is the matrix unique?

 implies  

Thus, a = 2 and b = –7. Hence, the unique matrix of the translation is

 

The image of Z(12, 7, 1) is (14, 0, 1) since