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

Verified step by step guidance

1. Identify the matrix A given as $[62-3]$.
2. Understand that the problem asks to find the matrix resulting from multiplying matrix A by the scalar -4, which means each element of A will be multiplied by -4.
3. Multiply each element of matrix A by -4: multiply 6 by -4, 2 by -4, and -3 by -4 separately.
4. Write the resulting matrix after scalar multiplication as $[-24-812]$ (do not calculate the final values here, just show the multiplication step).
5. Confirm that the resulting matrix has the same dimensions as matrix A, but with each element scaled by -4.

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 Notation and Elements

A matrix is a rectangular array of numbers arranged in rows and columns. Understanding the notation, such as A = [6 2 -3], helps identify individual elements to perform operations like addition, subtraction, or scalar multiplication.

Basic Matrix Operations

Basic operations on matrices include addition, subtraction, and scalar multiplication. These operations follow specific rules, such as element-wise addition or multiplying each element by a scalar, which are foundational for solving systems of equations and other algebraic problems.