Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

7. Systems of Equations & Matrices

Introduction to Matrices

College Algebra

7. Systems of Equations & Matrices

Introduction to Matrices

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2:39 minutes

Problem 43

Textbook Question

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

Verified step by step guidance

insert step 1> Identify the matrix B.

insert step 2> Multiply each element of matrix B by the scalar \( \frac{3}{2} \).

insert step 3> Write the resulting matrix after the scalar multiplication.

insert step 4> Ensure each element of the resulting matrix is simplified.

insert step 5> Verify the dimensions of the resulting matrix match those of matrix B.

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Key Concepts

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

Matrix Multiplication

Matrix multiplication involves taking two matrices and producing a new matrix by multiplying rows of the first matrix by columns of the second. The number of columns in the first matrix must equal the number of rows in the second matrix for the operation to be valid. The resulting matrix's dimensions are determined by the outer dimensions of the two matrices being multiplied.

Scalar Multiplication

Scalar multiplication is the process of multiplying each entry of a matrix by a scalar (a single number). This operation scales the matrix, affecting its size and direction but not its shape. For example, multiplying a matrix by 3 will triple each element, effectively enlarging the matrix while maintaining its structure.

Matrix Notation

Matrix notation is a way to represent a collection of numbers arranged in rows and columns. Each matrix is typically denoted by a capital letter (e.g., A, B) and can be used to perform various operations, such as addition, multiplication, and finding determinants. Understanding matrix notation is crucial for interpreting and manipulating matrices in algebra.