Question

For the following system of linear equations, 2x+3y−2z=3

3x+y+2z=11
4x+5y+3z=19
​Use row operations to determine the value of x,y,z.

Answer 1

To solve this system of linear equations using row operations, we first write the augmented matrix:

[2 3 -2 3]
[3 1 2 11]
[4 5 3 19]

We can use elementary row operations to transform this matrix into row echelon form. The goal is to get a matrix that looks like:

[1 a b c]
[0 1 d e]
[0 0 1 f]

where a, b, c, d, e, and f are constants.

Here are the steps:

1. Add -1.5 times the first row to the second row.
2. Add -2 times the first row to the third row.
3. Add -5 times the second row to the third row.
4. Multiply the second row by -1.
5. Add -2 times the second row to the first row.
6. Add -3 times the third row to the first row.
7. Add -2 times the third row to the second row.

The resulting matrix is:

[1 0 0 2]
[0 1 0 3]
[0 0 1 4]

So x = 2, y = 3, and z = 4.

I hope this helps! Let me know if you have any other questions.