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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1:46 minutes

Problem 14

Textbook Question

In Exercises 9 - 16, find the following matrices: a. A + BA = [6 2 - 3], B = [4 - 2 3]

Verified step by step guidance

Identify the matrices A and B: A = [6, 2, -3], B = [4, -2, 3].

Ensure that both matrices have the same dimensions for addition.

Add corresponding elements of matrices A and B.

Calculate the sum for each element: (6 + 4), (2 + (-2)), (-3 + 3).

Write the resulting matrix from the sums of corresponding elements.

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Key Concepts

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

Matrix Addition

Matrix addition involves combining two matrices of the same dimensions by adding their corresponding elements. For example, if A = [a11 a12 a13] and B = [b11 b12 b13], then A + B = [a11 + b11, a12 + b12, a13 + b13]. This operation is fundamental in linear algebra and is used in various applications, including solving systems of equations.

Element-wise Operations

Element-wise operations refer to performing calculations on corresponding elements of matrices. In the context of matrix addition, each element in the resulting matrix is the sum of the elements from the two matrices being added. Understanding this concept is crucial for accurately performing matrix operations and ensuring that the dimensions of the matrices align correctly.

Matrix Dimensions

Matrix dimensions indicate the number of rows and columns in a matrix, typically expressed as 'm x n' where m is the number of rows and n is the number of columns. For matrix addition to be valid, both matrices must have the same dimensions. In this case, both matrices A and B are 1 x 3 matrices, allowing for their addition.