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Identity Matrix: Definition, Properties, and Applications

CC.HSA.REI.C.8

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Notation of matrices

Adding and subtracting matrices

Scalar multiplication of matrices

Representing a linear system as a matrix

CC.HSA.REI.C.9

Matrix multiplication

The three types of matrix row operations

The Inverse of a 2 x 2 matrix

Solving linear systems using 2 x 2 inverse matrices

CC.HSA.SSE.B.4

Factor by taking out the greatest common factor

Factor by taking out GCF

Factor by grouping

Factoring difference of squares: \(x^2 - y^2\)

Factoring difference of squares: <katex>x^2 - y^2</katex>

Factoring difference of squares: x^2 - y^2

Geometric series

Geometric Series

CC.HSF.BF.A.2

Arithmetic sequences

Arithmetic series

Arithmetic series formula

Geometric sequences

Infinite geometric series

CC.HSF.BF.B.4

Finding the quadratic functions for given parabolas

Inverse functions

CC.HSF.IF.A.1

Domain and range of a function

Identifying functions

Function notation (advanced)

CC.HSF.IF.A.2

Function notation

Difference quotient: applications of functions

CC.HSF.IF.A.3

Greatest common factors (GCF)

Greatest Common Factor 2 Numbers

Greatest Common Factor 2 Numbers – Word Problem

Introduction to sequences

Sigma notation

CC.HSF.IF.B.5

Point of discontinuity

Even and odd functions

CC.HSF.LE.A.2

Graphing linear functions using table of values

CC.HSN.VM.A.1

Use sine ratio to calculate angles and sides (Sin = o / h)

Introduction to vectors

Magnitude of a vector

Direction angle of a vector

CC.HSN.VM.A.2

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Distance formula: <katex>d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}</katex>

Distance formula

Scalar multiplication of vectors

Equivalent vectors

CC.HSN.VM.B.4

Slope equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope equation: <katex>m = \frac{y_2-y_1}{x_2- x_1}</katex>

Adding and subtracting vectors in component form

Operations on vectors in magnitude and direction form

CC.HSN.VM.B.5

Slope intercept form:  y = mx + b

Slope intercept form: y = mx + b

Unit vector

CC.HSN.VM.C.10

Zero matrix

Identity matrix

The determinant of a 2 x 2 matrix

The determinant of a 3 x 3 matrix (General & Shortcut Method)

CC.HSN.VM.C.11

Transforming vectors with matrices

Transforming shapes with matrices

CC.HSN.VM.C.6

CC.HSN.VM.C.9

Properties of matrix multiplication

CC.HSS.CP.A.1

Set notation

Understanding How to Use Set Notation

Set builder notation

Intersection and union of 2 sets

Intersection and Union of 2 Sets

Intersection and union of 3 sets

Intersection and Union of 3 Sets

Introduction to probability

Identify the Probability — Word Problem

Compound Probability

Reading Probability Models

Probability

Organizing outcomes

Calculating Outcomes

CC.HSS.CP.A.2

Probability of independent events

Multiplication rule for 

Multiplication rule for "AND"

Multiplication Rule for "AND"

CC.HSS.CP.A.3

Conditional probability

CC.HSS.CP.A.5

Comparing experimental and theoretical probability

comparing experimental and theoretical probability

CC.HSS.CP.B.9

Permutations

Combinations

Probability involving permutations and combinations

CC.HSS.IC.A.1

Sampling methods

Sampling Methods

CC.HSS.IC.B.3

Census and bias

Census and Bias

Classifying Bias

CC.HSS.IC.B.4

Margin of error

Margin of Error

Making a confidence interval

Confidence intervals to estimate population mean

CC.HSS.ID.A.2

Median and mode

Median and Mode Table

Median and Mode – Word Problem

Median of an even length list

Median of an odd length list

Mean

Mean Word Problems

Find the Mean

Application of Means

Range and outliers

Range and Outlier Word Problems

Outlier Word Problems

Range Word Problems

Find the Range

Center of a data set: mean, median, mode

Spread of a data set - standard deviation & variance

CC.HSS.ID.A.3

Application of averages

Measures of Central Tendency — Word Problem

Find the Means — Data Tables

Find Mean and Mode — Data Table

Identify Outliers — Data Table

Shapes of distributions

CC.HSS.MD.A.1

Probability distribution - histogram, mean, variance & standard deviation

CC.HSS.MD.A.2

Properties of expectation

Properties of Expectation and Variance

Properties of Expectation

CC.HSS.MD.A.3

Binomial distribution

Binomial Distribution

Mean and standard deviation of binomial distribution

Interpreting Mean and Standard Deviation of Binomial

CC.HSS.MD.B.7

Type 1 and type 2 errors

Type 1 and Type 2 Errors

Discrete Math

math

Intro

Ex.1

Ex.2

In this lesson, we will learn about identity matrices. <a href='[[glossary.html|{"keyword":"Identity matrix"}]]'>Identity matrix</a> is an n by n matrix which all entries <a href='[[glossary.html|{"keyword":"Main Diagonal of a Matrix"}]]'>diagonal</a> from the top left to the bottom right are 1's, and the rest of the entries are 0. There are many types of identity matrices, as listed in the notes section. We will learn how to apply matrix operations with these such as adding, subtracting, and multiplying. Lastly, we will see that identities have a special property. If two matrices are multiplicative inverses, then multiplying them would give an identity matrix.

Identity Matrix

What is an identity matrix?

Scalar multiplication

Multiplying a matrix by a scalar