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

검증된 단계별 안내

Step 1: Understand the problem. You are asked to find the matrix A - B, which means subtracting matrix B from matrix A. Both matrices A and B are 3x3 matrices, so subtraction is possible element-wise.

Step 2: Recall the rule for matrix subtraction. For two matrices A = [a_ij] and B = [b_ij] of the same size, the difference A - B is a matrix C = [c_ij] where each element c_ij = 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: Subtract corresponding elements of B from A. For example, the element in the first row and first column of A - B is 2 - 6, the element in the first row and second column is -10 - 10, and so on for all elements.

Step 5: Write the resulting matrix after subtraction by placing each computed element in its corresponding position to form the matrix 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 Subtraction

Matrix subtraction involves subtracting corresponding elements of two matrices of the same dimensions. Each element in the resulting matrix is found by subtracting the element in matrix B from the element in matrix A at the same position.

Matrix Dimensions

For matrix operations like addition or subtraction to be valid, the matrices must have the same dimensions, meaning the same number of rows and columns. Here, both matrices A and B are 3x3, allowing element-wise subtraction.

Element-wise Operations

Element-wise operations apply arithmetic operations to each corresponding element in matrices. In subtraction, this means subtracting each element of matrix B from the corresponding element of matrix A to form the new matrix.