Unit 1 Matrix Algebra | Study Guide

University:
University of California, Berkeley
Course:
MATH W54 | Linear Algebra and Differential Equations
Academic year:

2021
Views:

282

Pages:

3
Author:

Raina Flores

Unit 1 Matrix Algebra ● Matrix ○ A matrix is a collection of numbers organized into rows and columns. ○ Matrices are referred to as capital letters. ■ Ex; Amxn ● Graphing Calculator instructions 1. Press [ALPHA][ZOOM] to create a matrix 2. Click [x–1] to identify the inverse of matrix A 3. Enter the constant matrix, B. 4. Press [ENTER] to evaluate the variable matrix, X. ● Example 1: The Alfred Company is a plastic container and wooden container maker. The following plastic containers were developed on a specific day: 900 with a capacity of 30 pounds (lb), 450 with a capacity of 10 pounds, and 200 with a capacity of 20 pounds. On the same day, the following wooden containers were produced: 530 with a capacity of 30 pounds, 670 with a capacity of 10 pounds, and 880 with a capacity of 20 pounds. Find a matrix 2 by 3 that represents this info. To represent the same data, find a 2 by 3 matrix (A) ● Operations with matrices ○ Scalar Multiplication ■ Increase each number in the matrix by the factor ■ Let’s call the matrix in the previous function matrix ‘A’ ● If they question was asking ‘What is 4A?’, you would just multiply each number in the matrix by 4. ○ Addition/subtraction ■ Dimensions of the matrices must match! ● This means if one matrix is 2x2 you cannot add it to a 3x2 matrix ○ Multiplication ■ When multiplying, you do rows x columns! ■ Associative and distributive properties apply to matrix multiplication, but NOT commutative property! ○ The Identity Matrix ■ Equivalent to multiplying by 1, you’ll always end up with the original matrix. ■ When multiplying by an identity matrix, you’ll have an I with a superscript that tells you how many rows and columns there are. ● Solving Linear Systems Using Inverse Matrices ○ The first column in the matrix is for the x value in the polynomial, the second is for the y, and the third is for the x