Let and . Find each of the following. See Examples 2 –4.
(3/2)B

Verified step by step guidance

First, identify the given vectors A and B. Since the problem statement is incomplete, ensure you have the components of vector B before proceeding.

Understand that the expression (3/2)B means you need to multiply each component of vector B by the scalar 3/2. This is called scalar multiplication of a vector.

Write the scalar multiplication formula: if $ B = \langle b_1, b_2, \ldots, b_n \rangle $, then $ \frac{3}{2} B = \left\langle \frac{3}{2} b_1, \frac{3}{2} b_2, \ldots, \frac{3}{2} b_n \right\rangle $.

Multiply each component of vector B by 3/2 separately to get the new vector components.

Express the resulting vector after scalar multiplication as your final answer for $ \frac{3}{2} B $.

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Key Concepts

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

Scalar Multiplication of Matrices

Scalar multiplication involves multiplying every element of a matrix by a constant (scalar). This operation scales the matrix without changing its dimensions, and is fundamental for matrix algebra and transformations.

Matrix Notation and Elements

Understanding matrix notation means recognizing how matrices are represented with rows and columns, and how to identify and manipulate individual elements. This is essential for performing operations like addition, multiplication, and scalar multiplication.

Order of Operations in Matrix Algebra

Matrix operations follow specific rules and order, similar to arithmetic. Knowing when and how to apply scalar multiplication before or after other operations ensures correct results, especially when combining matrices or performing multiple steps.

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