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

검증된 단계별 안내

Identify the matrix A given as

[\begin{matrix} 2 & - 10 & - 2 \\ 14 & 12 & 10 \\ 4 & - 2 & 2 \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, the element in the first row and first column (2) becomes

-4 \(\times\) 2 = -8

Apply this multiplication to all elements in matrix A to form the new matrix

-4A

Write the resulting matrix with all elements multiplied by -4, maintaining the same dimensions and order as matrix A.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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 Dimensions

Understanding matrix notation is essential; matrices are represented by brackets containing rows and columns. The dimensions (rows × columns) must be consistent for operations like addition or multiplication. Here, A and B are 3×3 matrices.

Matrix Operations in Algebra

Matrix operations such as addition, subtraction, and scalar multiplication follow specific rules. These operations are foundational in algebra for solving systems, transformations, and more. Recognizing how to apply these rules is key to manipulating matrices correctly.