Slide 1 Fundamentals of Engineering Analysis PowerPoint Presentation

Slide  1 Fundamentals of Engineering Analysis PowerPoint Presentation

2019-03-14 1K 1 0 0

Description

EGR . 1302 - . Determinants. Slide . 2. Determinants. “Eyeball” Method. 3 positive terms. 3 negative terms. - A Property of a Square Matrix. Slide . 3. Determinant of a 3x3. Let’s factor out the elements of the first row of the matrix, i.e.. ID: 756269

Embed code:

Download this presentation



DownloadNote - The PPT/PDF document "Slide 1 Fundamentals of Engineering Ana..." 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.

Presentations text content in Slide 1 Fundamentals of Engineering Analysis

Slide1

Slide 1

Fundamentals of Engineering Analysis

EGR

1302 -

Determinants

Slide2

Slide 2

Determinants

“Eyeball” Method

3 positive terms

3 negative terms

- A Property of a Square Matrix

Slide3

Slide 3

Determinant of a 3x3

Let’s factor out the elements of the first row of the matrix, i.e.

Slide4

Slide 4

Determinant of a 3x3

We can identify this construct as the “Cofactor”

Slide5

Slide 5

The Cofactor Matrix of a 3x3

The cofactor of any element is “the determinant formed by striking out the Row & Column of that element

Every element in a square matrix has a

cofactor

Slide6

Slide 6

The Cofactor Matrix of a 3x3

Sign of the Cofactor:

Caution: Do not forget the signs of the cofactors

Slide7

Slide 7

Determinant by Row Expansion

Row Expansion:

using the first row:

Slide8

Slide 8

Using the TI-89 to find Determinants

We had previously entered a matrix

and assigned it to the variable “a”

The calculator has the built-in function “det()“

Which calculates the determinant of a square matrix.

Slide9

Slide 9

Determinant by Row or Column Expansion

Select

Any

Row or Column to do the Expansion

Pick Column #1 to simplify the calculation due to the zero terms.

Slide10

Slide 10

Finding the Cofactor Matrix of A

Calculators and Computers obviously make this process easier.

Slide11

Slide 11

Rules for 2x2 Inverse and the Cofactor Matrix

1. Swap Main Diagonal

2. Change Signs on a

12

, a

213. Divide by detASimilar, but not quite

Slide12

Slide 12

Properties of Determinants

1. Determinant of the Transpose Matrix

det A = det A

T

Slide13

Slide 13

Properties of Determinants

2. Multiply a single Row (Column) by a Scalar - k

det B = k*det A

for

det B = 3*det A

Slide14

Slide 14

Properties of Determinants

3. If two Rows (Columns) are swapped, the sign changes

det B = -det A

swap

Recall:

4. Expansion by any Rows (Columns) equals the same Determinant

Slide15

Slide 15

Properties of Determinants

5. If two Rows (Columns) are equal, or the same ratio,

i.e., Row

1

= k*Row2

det A = 0 det B = 0 Col2 = 2*Col1

det A = 0 Row2 = Row1 The matrix A is “singular”

Recall Rule #3 to find A-1,divide by detA

But if detA=0,a unique solution does not exist

Slide16

Slide 16

Properties of Determinants

If a new matrix B is constructed from A

by adding K*row

j

to another rowi …

det B = det A

Construct D by creating a new Row 2

These are called Row (Column) Operations

Slide17

Slide 17

Finding the Determinant: Two Methods

2 + (-40) + (-6) – (-5) -12 –(-8) = -43

“Eyeball” Method

Row Expansion

1*(2-12) -2(-4+3) -5(8-1)

-10 + 2 -35 = -43

Slide18

Slide 18

Questions?


About DocSlides
DocSlides allows users to easily upload and share presentations, PDF documents, and images.Share your documents with the world , watch,share and upload any time you want. How can you benefit from using DocSlides? DocSlides consists documents from individuals and organizations on topics ranging from technology and business to travel, health, and education. Find and search for what interests you, and learn from people and more. You can also download DocSlides to read or reference later.