Use the given row transformation to change each matrix as indicated. See Sample 1. < 2x2 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 and Row 2.
2. Multiply each element of Row 1 by -4.
3. Add the result from the previous step to the corresponding elements of Row 2.
4. Replace Row 2 with the new values obtained from the addition.
5. Write down the new matrix with the transformed Row 2.

Key Concepts

Matrix Row Operations

Matrix row operations are techniques used to manipulate the rows of a matrix to achieve a desired form, such as row echelon form or reduced row echelon form. The three primary operations include swapping two rows, multiplying a row by a non-zero scalar, and adding a multiple of one row to another row. These operations are fundamental in solving systems of linear equations and performing matrix transformations.

Scalar Multiplication

Scalar multiplication involves multiplying each element of a matrix by a constant value, known as a scalar. In the context of the given question, multiplying row 1 by -4 means that every element in that row will be multiplied by -4. This operation is crucial for adjusting the values in a matrix to facilitate further calculations or transformations.

Row Addition

Row addition is a specific type of row operation where a multiple of one row is added to another row. This operation is used to eliminate variables in systems of equations or to simplify matrices. In the example provided, adding -4 times row 1 to row 2 modifies row 2 based on the values in row 1, which is essential for achieving the desired matrix form.