Table of contents

0. Review of Algebra4h 16m
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 19m
10. Combinatorics & Probability1h 45m

7. Systems of Equations & Matrices

Introduction to Matrices

College Algebra

7. Systems of Equations & Matrices

Introduction to Matrices

1:55 minutes

Problem 63

Textbook Question

Find each product, if possible. See Examples 5–7. <4x2 Matrix>

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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 multiplication to be possible. The resulting matrix's dimensions are determined by the number of rows from the first matrix and the number of columns from the second.

Dimensions of a Matrix

The dimensions of a matrix are defined by the number of rows and columns it contains, expressed as 'm x n' where 'm' is the number of rows and 'n' is the number of columns. Understanding the dimensions is crucial for determining compatibility for operations like addition and multiplication, as these operations have specific requirements regarding the sizes of the matrices involved.

Product of Matrices

The product of two matrices is a new matrix formed by the multiplication of the two original matrices. Each element in the resulting matrix is calculated as the sum of the products of corresponding elements from the rows of the first matrix and the columns of the second. This operation is fundamental in linear algebra and has applications in various fields, including computer graphics and systems of equations.