In Exercises 9 - 16, find the following matrices: c. - 4A

Verified step by step guidance

1. Identify matrix A as \( A = \begin{bmatrix} 3 & 1 & 1 \\ -1 & 2 & 5 \end{bmatrix} \).
2. Understand that the problem asks to find \( -4A \), which means multiplying every element of matrix A by -4.
3. Multiply each element of matrix A by -4: for example, multiply 3 by -4, 1 by -4, and so on for all elements.
4. Write the resulting matrix after multiplication, keeping the same dimensions as matrix A.
5. Verify that each element in the new matrix is correctly calculated as \( -4 \times \text{original element} \).

Key Concepts

Matrix Scalar Multiplication

Scalar multiplication involves multiplying every element of a matrix by a constant (scalar). For example, multiplying matrix A by -4 means each entry in A is multiplied by -4, resulting in a new matrix with scaled values.

Matrix Representation and Notation

A matrix is a rectangular array of numbers arranged in rows and columns, denoted by brackets. Understanding how to read and write matrices, such as A and B given here, is essential for performing operations like addition, subtraction, and scalar multiplication.

Element-wise Operations on Matrices

Matrix operations like addition, subtraction, and scalar multiplication are performed element-wise. This means each corresponding element in the matrix is operated on individually, which is crucial for correctly computing expressions like -4A.