Solve the following linear system by Gaussian elimination. x_(1)+3x_(2)+4x_(3)=9 -x_(1)-4x_(2)+5x_(3)=9 3x_(1)-7x_(2)+6x_(3)=15 x_(1)=i x_(2)=i x_(3)=i

To solve the given linear system using Gaussian elimination, we need to follow these steps:1. Write the augmented matrix for the system.2. Perform row operations to get an upper triangular form.3. Back-substitute to find the solutions.Given system: ### Step 1: Write the augmented matrix ### Step 2: Perform row operations to get an upper triangular form#### Row 1 (R1) remains the same: #### Eliminate from Row 2 (R2): #### Eliminate from Row 3 (R3): Now the matrix looks like this: #### Eliminate from Row 3 (R3): Now the matrix looks like this: ### Step 3: Back-substitution to find the solutionsFrom the third row: Substitute into the second row: Substitute and into the first row: ### Final Solution: