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

Previous problemNext problem

1:26 minutes

Problem 14

Textbook Question

In Exercises 9 - 16, find the following matrices: c. - 4AA = [6 2 - 3], B = [4 - 2 3]

Verified step by step guidance

Identify the matrix A given in the problem: A = [6, 2, -3].

Understand that the task is to find the matrix -4A, which means multiplying each element of matrix A by -4.

Multiply the first element of matrix A (6) by -4.

Multiply the second element of matrix A (2) by -4.

Multiply the third element of matrix A (-3) by -4.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

Key Concepts

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

Matrix Scalar Multiplication

Matrix scalar multiplication involves multiplying each element of a matrix by a scalar (a constant number). In this case, multiplying matrix A by -4 means that each element of A will be multiplied by -4, resulting in a new matrix. This operation is fundamental in linear algebra and is used to scale matrices.

Matrix Representation

Matrices are rectangular arrays of numbers arranged in rows and columns. Each matrix is defined by its dimensions, which indicate the number of rows and columns it contains. Understanding how to read and interpret matrices is crucial for performing operations such as addition, subtraction, and multiplication.

Element-wise Operations

Element-wise operations refer to performing calculations on corresponding elements of matrices. For example, when multiplying a matrix by a scalar, each element is treated independently. This concept is essential for understanding how to manipulate matrices and apply various operations in linear algebra.