Honors Advanced Algebra IITrigonometry Ms lee Essential Stuff Essential Question What is a matrix and how do we perform mathematical operations on matrices Essential Vocabulary Matrix ID: 549042
Download Presentation The PPT/PDF document "Introduction to Matrices" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Introduction to Matrices
Honors Advanced Algebra II/Trigonometry
Ms.
leeSlide2
Essential Stuff
Essential Question: What is a matrix, and how do we perform mathematical operations on matrices?
Essential Vocabulary:
Matrix
Scalar
Determinant
InverseSlide3
What is a matrix?
A
matrix
is
a rectangular array of numbers, symbols, or expressions arranged in rows and columns enclosed in a single set of brackets. A = The dimensions of a matrix are the number of horizontal rows and the number of vertical columns it has. NOTE!!: The number of rows always comes before the number of columns.
Slide4
Matrix Terminology
Each number, expression, or symbol in a matrix is called an
element
or an
entry. B = 4 Є BEntries are denoted by a variable and two subscripts (rows and columns). b1,2 = -7 b3,2 = 6 b2,1= 4=
Slide5
Adding and Subtracting Matrices
You can
add
or subtract matrices
if and only if
they have the same dimensions. In order to add or subtract two or more matrices, add their corresponding elements. Slide6
Adding and Subtracting Matrices
A + B = A+B
A - B = A-B
ExamplesSlide7
Scalar Multiplication
You can multiply a matrix by a constant called a
scalar
.
In order to perform scalar multiplication on a matrix, multiply each element in the matrix by the scalar.
ExamplesSlide8
Homework
Homework 2.1Slide9
Matrix Multiplication
Matrix multiplication has no operational counterpart in the real number system.
In order to multiply two matrices (matrix A and matrix B), the number of columns in A must be equal to the number of rows in matrix B.
Matrix A
Matrix B Matrix AB 3 x 2 2 x 4 3 x 4
equal
Dimensions of ABSlide10
When multiplying two matrices, A and B, multiply the entries of the first row of matrix A and the first column of matrix B, then add those products up to make the first entry in matrix AB.
Repeat this step until we have multiplied each row in matrix A with each column in matrix B.
Examples
Matrix MultiplicationSlide11
Determinant
The
determinant
is a real number associated with
SQUARE matrices. It tells us special things about the matrix useful in solving systems of equations, calculus, and more.Notation: det(A) = |A|Let A = , then det(A) = |A|=
= ad – bc.For any matrix larger than 2x2, the determinant will be found using calculator. Examples
Slide12
Inverse of Matrices:
Not every matrix has an inverse.
A matrix has an inverse if and only if it's determinant is
not
0.
A matrix is invertible if and only if ad – bc ≠ 0.Let A = be invertible.Then,
and
Slide13
Homework
Homework 2.2