Let A=[−2403]A = \left[ \begin{matrix} -2 & 4 \\ 0 & 3 \end{matrix} \right] and B=[−6240]B = \left[ \begin{matrix} -6 & 2 \\ 4 & 0 \end{matrix} \right] B=[−6420]. Find each of the following.-A + (1/2)B

Ch. 5 - Systems and Matrices

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Lial 13th Edition

Ch. 5 - Systems and Matrices

문제 47

6장, 문제 47

Let $A = [\begin{matrix} - 2 & 4 \\ 0 & 3 \end{matrix}]$ and $B = $\left$[ $\begin{matrix}$ -6 & 2 \\ 4 & 0 $\end{matrix}$ $\right$]$ . Find each of the following.
-A + (1/2)B

검증된 단계별 안내

Identify the vectors A and B given in the problem. Since the problem statement is incomplete, assume A and B are vectors with components, for example, A = (a_1, a_2) and B = (b_1, b_2).

Calculate the scalar multiplication of vector B by 1/2. This means multiplying each component of B by 1/2, resulting in ($\frac{1}{2}$b_1, $\frac{1}{2}$b_2).

Find the vector -A by multiplying each component of A by -1, resulting in (-a_1, -a_2).

Add the vectors -A and $\frac{1}{2}$B component-wise. This means adding the corresponding components: (-a_1 + $\frac{1}{2}$b_1, -a_2 + $\frac{1}{2}$b_2).

Write the final expression for -A + $\frac{1}{2}$B as a vector with the components found in the previous step.

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 of two matrices of the same dimensions. Scalar multiplication means multiplying every element of a matrix by a constant. Both operations are fundamental for combining matrices as in the expression -A + (1/2)B.

Negative of a Matrix

The negative of a matrix, denoted as -A, is found by multiplying every element of matrix A by -1. This operation reverses the sign of each element and is essential when subtracting or adding the negative of a matrix.

Matrix Dimensions and Compatibility

For matrix addition or subtraction, the matrices must have the same dimensions (same number of rows and columns). Ensuring A and B are compatible is crucial before performing operations like -A + (1/2)B to avoid undefined results.

Let A=[−2403]A = \(\left\)[ \(\begin{matrix}\) -2 & 4 \\ 0 & 3 \(\end{matrix}\) \(\right\)] and B=[−6240]B = \(\left\)[ \(\begin{matrix}\) -6 & 2 \\ 4 & 0 \(\end{matrix}\) \(\right\)] B=[−6420]. Find each of the following.-A + (1/2)B

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Matrix Addition and Scalar Multiplication

Negative of a Matrix

Matrix Dimensions and Compatibility

Let $A = [\begin{matrix} - 2 & 4 \\ 0 & 3 \end{matrix}]$ and $B = \(\left\)[ \(\begin{matrix}\) -6 & 2 \\ 4 & 0 \(\end{matrix}\) \(\right\)]$ . Find each of the following.
-A + (1/2)B