x y z rhs
1 1 2 3
2 1 6 3
0 3 4 13
multiply some number by r2 and add result to r3(2)
have to get o in r3 (1)-
steps:------------------
x y z rhs
1 1 2 3
2 1 6 3
0 3 4 13
multiply some number by r2 and add result to r3(2)
have to get o in r3 (1)-
steps:-----------------
answer quick
To get 0 in row 3 (r3), you need to perform row operations on the given system of equations. Here are the steps:
Step 1: Multiply some number by r2 and add the result to r3 to eliminate the x term in r3:
- Multiply r2 by a number so that when added to r3, the x term in r3 cancels out. In this case, since the x coefficient in r3 is already 0, you don't need to make any changes to r2.
- Add r2 to r3:
(r3) = (0 3 4 13) + (2 1 6 3)
= (2 4 10 16)
The system of equations after this step is:
x y z rhs
1 1 2 3
2 1 6 3
2 4 10 16
Step 2: We need to perform another row operation to eliminate the x term in r1. Since r1 and r2 have the same x coefficient, we can subtract r1 from r2, and then subtract r1 from r3:
- Subtract r1 from r2:
(r2) = (2 1 6 3) - (1 1 2 3)
= (1 0 4 0)
- Subtract r1 from r3:
(r3) = (2 4 10 16) - (1 1 2 3)
= (1 3 8 13)
The system of equations after this step is:
x y z rhs
1 1 2 3
1 0 4 0
1 3 8 13
Now, we have eliminated the x term in r3 and r1.