Algebra

[3 -1 | -1] [1 -5 | 6] --(-3R2+R1)--> ?

Step-by-step solution with explanation

Final Answer

Step-by-step solution

1

Identify the row operation to apply

The notation means we multiply Row 2 by , add it to Row 1, and replace Row 1 with the result. Row 2 stays the same.
2

Multiply Row 2 by negative three

We scale every entry in Row 2 by . This gives us the temporary row that we will add to Row 1.
3

Add scaled Row 2 to Row 1

We add each corresponding entry of the scaled row to Row 1. The first column becomes , which is the goal — eliminating a variable. Row 2 is unchanged.
4

Write the resulting augmented matrix

The new matrix has Row 1 replaced by and Row 2 staying as . The leading zero in Row 1 means the first variable has been eliminated from that row.

Understanding this problem

Learning Insight

Row operations on augmented matrices are legal because they mimic what you can do to both sides of a system of equations — multiplying an equation by a constant or adding two equations together never changes the solution set. The goal is to create zeros to isolate variables, a process called Gaussian elimination.

Quick Tip

Always work column by column from left to right. To eliminate the entry in row , column , multiply the pivot row by and add it to row .

Common Mistake

Students often forget to apply the scalar to the augmented (right-hand) side of the matrix — they correctly scale the coefficient columns but leave the answer column unchanged, giving a wrong result.