In Exercises 9 - 16, find the following matrices: d. - 3A + 2B

검증된 단계별 안내

Step 1: Understand the problem. You are asked to find the matrix expression \(-3A + 2B\), where \(A\) and \(B\) are given matrices.

Step 2: Multiply matrix \(A\) by the scalar \(-3\). This means multiplying every element of matrix \(A\) by \(-3\). For example, the element in the first row and first column of \(A\) is 2, so after multiplication it becomes \(-3 \times 2 = -6\). Do this for all elements of \(A\).

Step 3: Multiply matrix \(B\) by the scalar \(2\). This means multiplying every element of matrix \(B\) by \(2\). For example, the element in the first row and first column of \(B\) is 6, so after multiplication it becomes \(2 \times 6 = 12\). Do this for all elements of \(B\).

Step 4: Add the resulting matrices from Step 2 and Step 3. To add two matrices, add their corresponding elements. For example, add the element in the first row and first column of the scaled \(A\) matrix to the element in the first row and first column of the scaled \(B\) matrix.

Step 5: Write the resulting matrix from Step 4 as your final answer for \(-3A + 2B\).

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 and Scalar Multiplication

Matrix addition involves adding corresponding elements from two matrices of the same dimensions. Scalar multiplication means multiplying every element of a matrix by a constant. These operations are fundamental for combining matrices as in the expression -3A + 2B.

Matrix Dimensions and Compatibility

For matrix addition or subtraction, the matrices must have the same dimensions (same number of rows and columns). Here, both A and B are 3x3 matrices, so operations like -3A + 2B are valid and can be performed element-wise.

Order of Operations in Matrix Expressions

When evaluating expressions like -3A + 2B, scalar multiplication is performed first on each matrix, followed by matrix addition. This ensures the correct combination of matrices and accurate results.