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

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Identify the matrix A given as

[\begin{matrix} 1 & 3 \\ 3 & 4 \\ 5 & 6 \end{matrix}]

Understand that the problem asks to find the matrix

-4A

, which means multiplying every element of matrix A by -4.

Multiply each element of matrix A by -4: for example, multiply 1 by -4, 3 by -4, 3 by -4, and so on for all elements.

Write the resulting matrix after multiplication, keeping the same dimensions as matrix A (3 rows and 2 columns).

Double-check each multiplication to ensure accuracy and confirm that the negative sign is applied to all elements.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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 how to read and identify elements by their position (row, column) is essential for performing operations like scalar multiplication.

Properties of Matrices in Algebra

Matrices follow specific algebraic rules, such as distributive and associative properties. Recognizing these properties helps in manipulating matrices correctly during operations like addition, multiplication, and scalar multiplication.

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