MATH 51: October 19, 2010Let F =232,220,011,G =101,023,110.Find the matrix which changes F -coordinates to G-coordinates.We can solve this by writing each vector in F in G-coordinates.But we won’t. Instead, we go via E -coordinates. So we want to compute1 0 10 2 11 3 0−12 2 03 2 12 0 1.The RREF computation for the inverse goes like this:1 0 1 1 0 00 2 1 0 1 01 3 0 0 0 1subtract row 1 from row 31 0 1 1 0 00 2 1 0 1 00 3 −1 − 1 0 1∗ subtract row 2 from row 31 0 1 1 0 00 2 1 0 1 00 1 −2 − 1 −1 1swap rows 2 and 31 0 1 1 0 00 1 −2 − 1 −1 10 2 1 0 1 0subtract 2x row 2 from row 31 0 1 1 0 00 1 −2 − 1 −1 10 0 5 2 3 −21MATH 51: October 19, 2010 2divide row 3 by 51 0 1 1 0 00 1 −2 −1 −1 10 0 1 2/5 3/5 −2/5subtract row 3 from row 11 0 0 3/5 −3/5 2/50 1 −2 −1 −1 10 0 1 2/5 3/5 −2/5subtract (-2)x row 3 from row 21 0 0 3/5 −3/5 2/50 1 0 −1/5 1/5 1/50 0 1 2/5 3/5 −2/5Now we have the identity on the left hand side, which means the right handside is the inverse:1 0 10 2 11 3 0−1=153 −3 2−1 1 12 3 −2So the matrix we’re after is153 −3 2−1 1 12 3 −22 2 03 2 12 0 1=151 0 −13 0 29 10 1You can check that the other method gives the same answer. For example,f2= 2g3, so[f2]G=002, which is indeed the second column of this matrix.∗Here I deviated from the usual algorithm because I wanted to get a 1 in thesecond column to use as a pivot, to avoid dividing by 2.Amy Pang,
View Full Document
Unlocking...