342 Review Questions and Answers
Question 19-4
Using the rules outlined above, how can we get the matrix from Answer 19-1 into echelon form,
and then reduce the sizes of the elements to make the matrix easier to work with later?Answer 19-4
Here’s the matrix again, for reference:4 − 4 − 4 8
− 1 255(^2) − 1 413
We can multiply the second row by 2 to get
(^4) − 4 − 4 8
− 2 41010
2 − 1 413
Now we can add the second and third rows and then replace the third row with the sum,
obtaining
(^4) − 4 − 4 8
− 2 41010
0 3 14 23
If we divide the first row by 2, we get
(^2) − 2 − 2 4
− 2 41010
0 3 14 23
Adding the first two rows and then replacing the second row with the sum, we obtain
2 − 2 − 2 4
02814
0 3 14 23
We can multiply the second row by −3 and the third row by 2 to get
2 − 2 − 2 4
(^0) − 6 − 24 − 42
0 6 28 46