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

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

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Lial 13th Edition

Ch. 5 - Systems and Matrices

Problem 41

Chapter 6, Problem 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

Verified step by step guidance

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.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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