344 Review Questions and Answers
Adding the first and third rows and then replacing the first row with the sum gives us1006
0147(^00) − 3 − 3
Now let’s multiply the third row by 4/3. We get
1006
0147
(^00) − 4 − 4
Adding the second and third rows and then replacing the second row with the sum, we obtain
the diagonal matrix
1006
0103
00 − 4 − 4
Question 19-6
How can we get the last matrix in Answer 19-5 into unit diagonal form?
Answer 19-6
This is easy, because we reduced our numbers along the way. We can divide the third row of
the last matrix in Answer 19-5 by −4 to get
1006
0103
0011
Question 19-7
What is the solution to the original three-by-three system based on Answer 19-6?
Answer 19-7
The solution can be read down the last column for x,y, and z in order:
x= 6
y= 3
z= 1
We know these values are correct, because they are the same values we found and verified in
the previous section for the same original three-by-three linear system.