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. 2A

Ch. 5 - Systems and Matrices

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Lial 13th Edition

Ch. 5 - Systems and Matrices

문제 41

6장, 문제 41

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.
2A

검증된 단계별 안내

First, identify the matrix A given in the problem. Since the problem statement is incomplete, ensure you have the matrix A before proceeding.

Recall that multiplying a matrix by a scalar means multiplying every element of the matrix by that scalar. Here, the scalar is 2.

Write the expression for 2A as $2 \times A$.

Multiply each element of matrix A by 2. For example, if an element in A is $a_{ij}$, then the corresponding element in 2A will be $2 \times a_{ij}$.

Write down the resulting matrix after multiplication, which is the matrix 2A.

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 Scalar Multiplication

Scalar multiplication involves multiplying every element of a matrix by a constant (scalar). For example, if A is a matrix and k is a scalar, then kA is obtained by multiplying each entry of A by k. This operation changes the magnitude of the matrix but not its dimensions.

Matrix Notation and Dimensions

Understanding matrix notation is essential to identify the size and elements of a matrix. The dimensions (rows × columns) determine how operations like addition or multiplication can be performed. Properly interpreting the given matrices A and B is crucial before performing any calculations.

Basic Matrix Operations

Basic matrix operations include addition, subtraction, and scalar multiplication. Knowing how to perform these operations correctly is fundamental in algebra. For example, scalar multiplication is different from matrix multiplication and requires applying the scalar to each element individually.

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. 2A

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Matrix Scalar Multiplication

Matrix Notation and Dimensions

Basic Matrix Operations

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.
2A