658 Worked-Out Solutions to Exercises: Chapters 11 to 19
Now let’s multiply the second row by 13 and the third row by 4. That gives us10 − 3 16 2(^052) − 13 − 26
(^0) − 52 24 − 32
Adding the second row to the third and then replacing the third row with the sum, we get
(^10) − 3 16 2
(^052) − 13 − 26
0011 − 58
This matrix is in echelon form.
- We want to put the matrix from solution to Prob. 4 into diagonal form. We can
multiply the second row by 11 and the third row by 13 to obtain
(^10) − 3 16 2
0 572 − 143 − 286
0 0 143 − 754
Adding the second row to the third and then replacing the second row with the sum,
we get
10 − 3 16 2
0 572 0 −1,040
(^00143) − 754
Now let’s multiply the first row by 572 and the second row by 3. That produces
5,720 −1,716 9,152 1,144
0 1,716 (^0) −3,120
(^00143) − 754
Adding the first row to the second and then replacing the first row with the sum
gives us
5,720 0 9,152 −1,976
0 1,716 (^0) −3,120
0 0 143 − 754