Part Two 343Adding the second row to the third and then replacing the third row with the sum, we get
2 − 2 − 2 4(^0) − 6 − 24 − 42
0044
This matrix is in echelon form. We can reduce the sizes of the numbers in this matrix, making
it easier to work with as we continue the game. Let’s divide the first row by 2, the second row
by 6, and the third row by 4, getting
1 − 1 − 1 2
0 − 1 − 4 − 7
0011
Question 19-5
Using the rules of the matrix morphing game, how can we get the last matrix in Answer 19-4
into diagonal form?
Answer 19-5
Multiplying the second row of the echelon-form matrix we just derived by −1, we get
(^1) − 1 − 1 2
0147
0011
Adding the first row to the second, and then replacing the first row with the sum, we obtain
1039
0147
0011
If we multiply the third row by −3, we get
1039
0147
(^00) − 3 − 3