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Master Matrix Multiplication: Rules, Examples, and Applications

NY.A-APR.C.5+

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Pascal's triangle

Pascal's Triangle

Pascal"s Triangle

Pascal"s triangle

Binomial theorem

Determining the equation of a polynomial function

NY.A-APR.D.7+

Descartes&apos; rule of signs

Descartes' Rule of Signs

Descartes' rule of signs

Descartes" rule of signs

Multiplying rational expressions

Multiplying Rational Expressions

Multiplying Rational Expressions in Factored Form

Dividing rational expressions

Dividing Rational Expressions

Dividing Rational Expressions in Factored Form

Negative exponent rule

NY.F-BF.B.5+

What is a logarithm?

Logarithms and Exponential Growth

Understanding Logarithms through Exponential Growth

Understanding Logarithms

Converting from logarithmic form to exponential form

Evaluating logarithms without a calculator

Common logarithms

Natural log: ln

Evaluating logarithms using change-of-base formula

Converting from exponential form to logarithmic form

Solving exponential equations with logarithms

Product rule of logarithms

NY.F-TF.A.3+

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Find the exact value of trigonometric ratios

NY.F-TF.C.8+

Pythagorean identities

NY.F-TF.C.9+

Sum and difference identities

Sum and Difference Identities

Double-angle identities

Cofunction identities

NY.G-SRT.D.10+

Law of sines

Ambiguous case: SSA triangles

Law of cosines

NY.G-SRT.D.11+

Applications of the sine law and cosine law

NY.G-SRT.D.9+

Area of triangles: 1/2 a*b sin(C)

NY.N-CN.A.3+

Complex conjugates

Complex Conjugates

Distance and midpoint of complex numbers

Angle and absolute value of complex numbers

NY.N-CN.B.4+

Polar form of complex numbers

NY.N-CN.B.5+

Operations on complex numbers in polar form

NY.N-CN.B.6+

Midpoint formula: \(M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)\)

Midpoint formula

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)</katex>

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

NY.N-CN.C.8+

Solving polynomials with the unknown "b" from ax^2 + bx + c

Factoring polynomials: ax^2 + bx + c

Factoring Polynomials: ax^2 + bx + c

Factoring perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

Factoring perfect square trinomials

Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)

Find the difference of squares

Solving polynomials with unknown coefficients

Factoring polynomials: x^2 + bx + c

Applications of polynomials: x^2 + bx + c

NY.N-CN.C.9+

Word problems of polynomials

Fundamental theorem of algebra

NY.N-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

NY.N-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

NY.N-VM.A.3+

Word problems on vectors

Word problems relating guy wire in trigonometry

NY.N-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

NY.N-VM.B.5+

Slope intercept form:  y = mx + b

Slope intercept form: y = mx + b

Unit vector

NY.N-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)

The Inverse of a 2 x 2 matrix

NY.N-VM.C.11+

Transforming vectors with matrices

Transforming shapes with matrices

NY.N-VM.C.12+

Finding the transformation matrix

NY.N-VM.C.6+

Notation of matrices

Adding and subtracting matrices

NY.N-VM.C.7+

Scalar multiplication of matrices

NY.N-VM.C.8+

Matrix multiplication

The three types of matrix row operations

NY.N-VM.C.9+

Properties of matrix multiplication

Plus (+) Standards

math

Intro

Ex.1

Ex.2

Ex.3

In this lesson, we will learn how to multiply a matrix with another matrix. But we will learn about n-tuples first. An n-tuple is an ordered list of n numbers. Multiplying an n-tuple by another n-tuple is called the dot product. The dot product is the summation of all product of each corresponding entries. To multiply a matrix with another matrix, we have to think of each row and column as a n-tuple. Each entry will be the dot product of the corresponding row of the first matrix and corresponding column of the second matrix.  For example, if your entry is at the 3rd row and 4th column, then you have to take the dot product of the 3rd row of the first matrix and 4th column of the second matrix. Note that not all matrices can be multiplied.

Multiplying a matrix by another matrix

How to multiply two matrices together