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Ch. 5 - Systems and Matrices
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 5 - Systems and MatricesProblem 43
Chapter 6, Problem 43

Let Matrix A displayed as a 2x2 matrix with elements -2, 4 in the first row and 0, 3 in the second row. and . Find each of the following. See Examples 2 –4.
(3/2)B

Verified step by step guidance
1
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.
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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.
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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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Related Practice
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Determine the system of equations illustrated in each graph. Write equations in standard form.

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Let and . Find each of the following. See Examples 2 –4.

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Graph the solution set of each system of inequalities.

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Determine the system of equations illustrated in each graph. Write equations in standard form.

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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 \(\end{matrix}\) \(\right\)]. Find each of the following.

2A

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