Algebra/Simultaneous linear equation with three unknowns
Solving simultaneous linear equation with three unknows is a damn knotty problem to me. Though, with the help of determinant, I can solve it effectively. But now, I don't wanna use determinants anymore. Thus, I've tried an alternative however to no avail. Pls. Prof. Treat me like a novice by solving the question below without using inverse matrix or determinants:
explain thoroughly how you solve it!
To solve each of them, I write down the problem in matrix format.
Once this has been done, I get a 1 in the 1st element of the 1st by dividing that row by 3.
I then get a zero in each cell below that by subtracting off the appropriate multiple of row 1.
For the 1st step, I divide row 1 by 3, subtract 4/3 for the 2nd row, and subtract 2/3 from the 3rd row. I also do it to the solutions. This gives
1 0.6667 -0.3333 6.3333
0 -3.6667 3.3333 -21.3333
0 2.6667 -4.3333 19.3333
In the next step, I multiply the 2nd row by -3/11. This puts a 1 in the place of -3.6667.
I multiply the 2nd row by 1/11 and add that to the 1st row. I multiply the 2nd row by 8/11 and add it the 3rd row. This gives a zero in the second column. The result is
1 0 0.2727 2.4545
0 1 -0.9091 5.8182
0 0 -1.9091 3.8182
To get a 1 in the 3rd position of the 3rd row, multiply that row by -11/21.
Add -10/21 of the 3rd row to the 2nd row. Add -1/7 of the 3rd row to the 1st row.
The solution turns out to be 3, 4, -2.
This is how to do the 2nd problem as well.