Answer :
Answer:
The solution to the given linear system is x₁ = 1265.34, x₂ = -571.67, x₃ = -64.67.
Step-by-step explanation:
To solve the linear system using Gaussian elimination, we start with the augmented matrix:
[ 1 4 4 | -16 ]
[-1 -5 5 | -19 ]
[ 3 7 6 | -9 ]
We'll perform row operations to transform the augmented matrix into row-echelon form.
Step 1: Swap rows R1 and R2:
[-1 -5 5 | -19 ]
[ 1 4 4 | -16 ]
[ 3 7 6 | -9 ]
Step 2: Multiply R1 by -1:
[ 1 5 -5 | 19 ]
[ 1 4 4 | -16 ]
[ 3 7 6 | -9 ]
Step 3: Subtract R1 from R2 and R3:
[ 1 5 -5 | 19 ]
[ 0 -1 9 | -35 ]
[ 0 -8 21 | -66 ]
Step 4: Multiply R2 by -1:
[ 1 5 -5 | 19 ]
[ 0 1 -9 | 35 ]
[ 0 -8 21 | -66 ]
Step 5: Add 5 times R2 to R1:
[ 1 0 -50 | 184 ]
[ 0 1 -9 | 35 ]
[ 0 -8 21 | -66 ]
Step 6: Add 8 times R2 to R3:
[ 1 0 -50 | 184 ]
[ 0 1 -9 | 35 ]
[ 0 0 -3 | 194 ]
Step 7: Divide R3 by -3:
[ 1 0 -50 | 184 ]
[ 0 1 -9 | 35 ]
[ 0 0 1 | -64.67 ]
Step 8: Add 50 times R3 to R1 and 9 times R3 to R2:
[ 1 0 0 | 1265.34 ]
[ 0 1 0 | -571.67 ]
[ 0 0 1 | -64.67 ]
The row-echelon form of the augmented matrix is obtained. Now, we can read the solutions of the linear system directly:
x₁ = 1265.34
x₂ = -571.67
x₃ = -64.67
know more about linear system : brainly.com/question/26544018
#SPJ11
