Use the given row transformation to change each matrix as indicated. See Sample 1. < 3x3 Matrix > ; 4 times row 1 added to row 2

Verified step by step guidance

1. Identify the given matrix and label the rows as Row 1, Row 2, and Row 3.
2. Multiply each element of Row 1 by 4. This is the scalar multiplication step.
3. Add the resulting values from the previous step to the corresponding elements of Row 2. This is the row addition step.
4. Replace the original Row 2 with the new values obtained from the addition.
5. Write down the new matrix with the updated Row 2, while Row 1 and Row 3 remain unchanged.

Key Concepts

Matrix Operations

Matrix operations involve various manipulations of matrices, including addition, subtraction, and scalar multiplication. In this context, the operation specified is a row transformation, which alters the rows of a matrix to achieve a desired form, often used in solving systems of equations or finding inverses.

Row Transformation

Row transformation refers to the process of applying specific operations to the rows of a matrix. Common transformations include swapping rows, multiplying a row by a scalar, and adding a multiple of one row to another. These transformations are fundamental in techniques like Gaussian elimination, which simplifies matrices for easier analysis.

Scalar Multiplication

Scalar multiplication involves multiplying each element of a matrix by a constant (scalar). In the given question, multiplying row 1 by 4 before adding it to row 2 is an example of this operation. This concept is crucial for understanding how to manipulate matrices effectively during row transformations.