Homework SourseSolve the following system of linear equations Write you ans
Solve the following system of linear equations. Write you answer in parametric form.
x1 + 2x2 + x4 =3
3x1 + 6x2 + 6x3 + 21x4 6x5 =-9
x1 + 2x2 + x3 + 4x4 + x5 =0
4x1 + 8x2 + 6x3 + 22x4 6x5 =6
Solution
IF WE solve:
x1 + 2x2 + x4 =3
3x1 + 6x2 + 6x3 + 21x4 6x5 =-9
x1 + 2x2 + x3 + 4x4 + x5 =0
4x1 + 8x2 + 6x3 + 22x4 6x5 =6
equations we will get 3equations
3x1+2x2-x3+6x5=12
3x1+6x2-x3-x5=12
3x1+6x2-x3+x5=12
and solve this and got
can be transformed by a sequence of elementary row operations to the matrix
The reduced row echelon form of the augmented matrix is
which corresponds to the system
No equation of this system has a form zero = nonzero; Therefore, the system is consistent.
The leading entries in the matrix have been highlighted in yellow.
A leading entry on the (i,j) position indicates that the j-th unknown will be determined using the i-th equation.
Those columns in the coefficient part of the matrix that do not contain leading entries, correspond to unknowns that will be arbitrary. The system has infinitely many solutions:
i,e x4=x5.
then x4=3-x1-2x2
| Step 1: Transform the augmented matrix to the reduced row echelon form (Show details) |
