In Exercises 9 - 16, find the following matrices: a. A + B

검증된 단계별 안내

Step 1: Understand that to find the sum of two matrices A and B, both matrices must have the same dimensions. Here, both A and B are 3x3 matrices, so addition is possible.

Step 2: Recall that matrix addition is performed by adding corresponding elements from each matrix. That is, if A = [a_ij] and B = [b_ij], then A + B = [a_ij + b_ij].

Step 3: Write down the elements of matrices A and B clearly: A = \(\begin{bmatrix}\) 2 & -10 & -2 \\ 14 & 12 & 10 \\ 4 & -2 & 2 \(\end{bmatrix}\), B = \(\begin{bmatrix}\) 6 & 10 & -2 \\ 0 & -12 & -4 \\ -5 & 2 & -2 \(\end{bmatrix}\)

Step 4: Add each corresponding element: - For the element in the first row, first column: 2 + 6 - For the element in the first row, second column: -10 + 10 - Continue this process for all elements in the matrices.

Step 5: After adding all corresponding elements, write the resulting matrix as the sum A + B.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

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주요 개념

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

Matrix Addition

Matrix addition involves adding corresponding elements from two matrices of the same dimensions. Each element in the resulting matrix is the sum of elements in the same position from the original matrices. This operation is only defined when both matrices have the same number of rows and columns.

Matrix Dimensions

Matrix dimensions are expressed as rows × columns and determine the size of a matrix. For matrix addition, both matrices must have identical dimensions to ensure each element pairs correctly. Understanding dimensions helps verify if operations like addition or multiplication are valid.

Element-wise Operations

Element-wise operations apply a mathematical operation to each corresponding element of matrices. In addition, subtraction, or scalar multiplication, each element is treated independently. This concept is fundamental for performing matrix addition accurately.