![Rectangular
Coordinate
Sys tem
Relations and
Functions
Representations of
Relations and
Functions
Ordered Pairs
Equations/
Formulas
Domain and
Dependent
Independent
Variables
Slope and
Intercepts
6 5 4 3 2 1
7 8 0 β1 2 0
0 2 9 1 2 4
1
Paper #3a
CARYL MAE S. PUERTOLLANO
Subject: ICT in Mathematics Education
Professor: Ms. Rosemarie Galvez
* Create a Handout using MS Word
1. SmartArt
Here is a sample map of the lessons that will be covered in this module:
2a. Linear Algebra
Mapping
Diagram
Table
Graphs
Range
and
Appl ications
PARTITION OF MATRICES; BLOCK MULTIPLICATION
Linear
Functions
We now consider the following partitioned matrices of the same size to see how the operations work
in practice:
ν΄ = [
1 2 3 4 6 0
7 8 0 β3 1 6
0 2 9 1 2 4
], ν΅ = [
0 2 β1 0 β3 5
1 β2 4 β2 2 β5
4 β4 6 1 0 β4
], νΆ =
[
]
Now, A + B can be computed blockwise as A and B are partitioned the same way with
corresponding blocks or submatrices having the same sizes. However, even though A and C are](https://image.slidesharecdn.com/paper3apuertollano-141010211804-conversion-gate01/85/paper3a-puertollano-1-320.jpg)
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Paper3a puertollano
- 1. Rectangular Coordinate Sys tem Relations and Functions Representations of Relations and Functions Ordered Pairs Equations/ Formulas Domain and Dependent Independent Variables Slope and Intercepts 6 5 4 3 2 1 7 8 0 β1 2 0 0 2 9 1 2 4 1 Paper #3a CARYL MAE S. PUERTOLLANO Subject: ICT in Mathematics Education Professor: Ms. Rosemarie Galvez * Create a Handout using MS Word 1. SmartArt Here is a sample map of the lessons that will be covered in this module: 2a. Linear Algebra Mapping Diagram Table Graphs Range and Appl ications PARTITION OF MATRICES; BLOCK MULTIPLICATION Linear Functions We now consider the following partitioned matrices of the same size to see how the operations work in practice: ν΄ = [ 1 2 3 4 6 0 7 8 0 β3 1 6 0 2 9 1 2 4 ], ν΅ = [ 0 2 β1 0 β3 5 1 β2 4 β2 2 β5 4 β4 6 1 0 β4 ], νΆ = [ ] Now, A + B can be computed blockwise as A and B are partitioned the same way with corresponding blocks or submatrices having the same sizes. However, even though A and C are
- 2. matrices of the same size (so A + C can be computed adding elements entrywise) A + C cannot be computed blockwise as the blocks of A and C are not comparable. 2b. Number Theory Properties of Summation 1. Ξ£ ν νν =1 = ν + ν + β― + ν = νν. 2. Ξ£ νν₯ν = νΞ£ ν₯ν . νν =1 2 νν =1 3. Ξ£ (ν₯ν + ν¦ν ) = Ξ£ ν₯ν + Ξ£ ν¦ν . νν =1 νν = 1 νν =ν 2c. Algebra Simplifying Rational Algebraic Expression ν₯2+3ν₯+2 ν₯2β1 Solution: ν₯2+3ν₯+2 ν₯2β1 = (ν₯+1)(ν₯+2) (ν₯+1)(ν₯β1) = ν₯+2 ν₯β1 2d. Calculus Evaluate β« ν₯2 ν₯3 +1 νν₯ 1 0 Solution: ν’ = ν₯ 3 + 1 νν’ = 3ν₯ 2νν₯ νν’ 3ν₯2 = νν₯ β« ν₯ 2 ν₯ 3 + 1 νν₯ = β« ν₯ 2 ν’ β νν’ 3ν₯ 2 = 1 3 β« 1 ν’ νν’ = What factoring method is used in this step? 1 3 ν₯=1 ν₯=0 νν|ν’| = 1 3 1 νν|ν₯ 3 + 1|| 0 ν₯=1 ν₯=0 1 0 = 1 3 νν|1 + 1| β 1 3 νν|0 + 1| = 1 3 νν|2| β 1 3 νν|1| = 1 3 νν|2| β 0 = 1 3 νν|2|
- 3. 3 2e. Trigonometry The graph of ν¦ = ν ννν₯ is shown below. 3. Geometric figures with labels. 1. Name the parts of the circle. F G H D K L M A B C E 1 -1 ν 2 3ν 2ν 3ν 2 β β β