Find the following matrices: - 3A + 2B A=[311−125],B=[2−36−31−4]A = \begin{bmatrix} 3 & 1 & 1 \\ -1 & 2 & 5 \end{bmatrix} , B = \begin{bmatrix} 2 & -3 & 6 \\ -3 & 1 & -4 \end{bmatrix}A=[3−11215],B=[2−3−316−4]

Ch. 6 - Matrices and Determinants

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Blitzer 8th Edition

Ch. 6 - Matrices and Determinants

문제 12d

7장, 문제 12d

Find the following matrices: - 3A + 2B
$A = $\begin{bmatrix}$ 3 & 1 & 1 \\ -1 & 2 & 5 $\end{bmatrix}$ , B = $\begin{bmatrix}$ 2 & -3 & 6 \\ -3 & 1 & -4 $\end{bmatrix}$$

검증된 단계별 안내

First, write down the matrices A and B clearly: $A = \begin{bmatrix} 3 & 1 \\ 1 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 2 \\ -3 & 6 \end{bmatrix}$.

Next, multiply matrix A by the scalar -3. This means multiplying each element of A by -3: $-3A = -3 \times \begin{bmatrix} 3 & 1 \\ 1 & 2 \end{bmatrix} = \begin{bmatrix} -3 \times 3 & -3 \times 1 \\ -3 \times 1 & -3 \times 2 \end{bmatrix}$.

Then, multiply matrix B by the scalar 2. Multiply each element of B by 2: $2B = 2 \times \begin{bmatrix} 1 & 2 \\ -3 & 6 \end{bmatrix} = \begin{bmatrix} 2 \times 1 & 2 \times 2 \\ 2 \times (-3) & 2 \times 6 \end{bmatrix}$.

After finding $-3A$ and \$2B$, add the two resulting matrices element-wise: $-3A + 2B = \begin{bmatrix} (-3 \times 3) + (2 \times 1) & (-3 \times 1) + (2 \times 2) \\ (-3 \times 1) + (2 \times (-3)) & (-3 \times 2) + (2 \times 6) \end{bmatrix}$.

Finally, simplify each element in the resulting matrix to get the final matrix 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 Subtraction

Matrix addition and subtraction involve combining corresponding elements from two matrices of the same dimensions. To add or subtract matrices, each element in one matrix is added to or subtracted from the element in the same position in the other matrix.

Scalar Multiplication of Matrices

Scalar multiplication involves multiplying every element of a matrix by a constant (scalar). This operation scales the matrix by the scalar value, changing the magnitude of each element but not the matrix's dimensions.

Matrix Dimensions and Compatibility

For matrix operations like addition, subtraction, or scalar multiplication, the matrices must have the same dimensions (same number of rows and columns). Ensuring dimension compatibility is essential before performing these operations.

Find the following matrices: - 3A + 2B A=[311−125],B=[2−36−31−4]A = \(\begin{bmatrix}\) 3 & 1 & 1 \\ -1 & 2 & 5 \(\end{bmatrix}\) , B = \(\begin{bmatrix}\) 2 & -3 & 6 \\ -3 & 1 & -4 \(\end{bmatrix}\)A=[3−11215],B=[2−3−316−4]

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Matrix Addition and Subtraction

Scalar Multiplication of Matrices

Matrix Dimensions and Compatibility

Find the following matrices: - 3A + 2B
$A = \(\begin{bmatrix}\) 3 & 1 & 1 \\ -1 & 2 & 5 \(\end{bmatrix}\) , B = \(\begin{bmatrix}\) 2 & -3 & 6 \\ -3 & 1 & -4 \(\end{bmatrix}\)$