Have some fun with the terms used in maths...
1) Doing multiplication without tables ===> Doing the maths problems on the floor
2) Using integration ===> Discussing with classmates and copying relevant answers
3) Using differentiation ===> Sorting out what can be done and what can't
4) Finding partial fractions ===> allowed to complete the computation partially
5) Calculating standard deviation ===> finding out how many more marks to hit standard pass grade
Caution:
Do not take this too serious, otherwise ....... you will really have to check your standard deviation.
.
Monday, 22 September 2008
Wednesday, 17 September 2008
Multiplication of Matrices
As do normal number multiplication, matrices themselves, also have their set of multiplication.
They are however done in another interesting way.
This is so since a matrix consists of a set of numbers within it.
Therefore multiplying matrices are not so straight forward as normal numbers.
But do rest assure that there is nothing new, it is still simple multiplication ( and addition / subtraction).
Maths is simple and interesting, remember? Read on for the steps and caution points.
Below I show multiplication using 2 matrices of the 2 x 2 order.
Do note that I have presented the steps first, leaving out the technical computation later on in this post (below the diagram).
See below for the steps:
.
They are however done in another interesting way.
This is so since a matrix consists of a set of numbers within it.
Therefore multiplying matrices are not so straight forward as normal numbers.
But do rest assure that there is nothing new, it is still simple multiplication ( and addition / subtraction).
Maths is simple and interesting, remember? Read on for the steps and caution points.
Below I show multiplication using 2 matrices of the 2 x 2 order.
Do note that I have presented the steps first, leaving out the technical computation later on in this post (below the diagram).
See below for the steps:
- element "K" is obtained from the first row of left matrix and the first column of the next matrix,
- element "L" is obtained using first row of left matrix and SECOND column f next matrix.
- element "M" is obtained using SECOND row of left matrix and first column of next matrix.
- element "P" is using second row and column of the respective matrices.
These sequence is of utmost importance. Why?
By not following the sequence to obtain the final elements, the numbers will be simply messed up! This is a very common mistake among students of matrices.
It is mental discipline to systematically derive the elements in the appropriate positions.
Next, let us go into getting the actual number for the final elements. Here we go...
Elements "K" = (4 x a) + (2 x c)
Element "L" = (4 x b) + (2 x d)
Element "M" = (1 x a) + (5 x c)
Element "N" = (1 x b) + (5 x d) ===> There is it, you have gotten all the elements!
There is nothing difficult, right? Matrix study is one of the simplest topics in maths.
Have fun!
.
Thursday, 11 September 2008
Math Challenge (10)
It is time for us to play some math game.
You do not need a university degree to handle this game.
Everyone can play. It is meant to exercise your brain, nothing taxing.
What is this game about?
Challenge
There is a series of numbers that you have to add mathematical operators (+, -, / , x or brackets) to. The addition of these operators has to satisfy the end result though.
Example:
2 2 2 2 = 0 => Solution is 2 + 2 - 2 - 2 = 0
2 2 2 2 = 1
2 2 2 2 = 2
2 2 2 2 = 3
2 2 2 2 = 4
2 2 2 2 = 5
2 2 2 2 = 6
2 2 2 2 = 7
2 2 2 2 = 8
2 2 2 2 = 9
Nothing difficult, right? It is just to get your brain moving, otherwise it will go rusty.
Enjoy yourself.
You may also alter the list to include other numbers.
4 4 5 5 = 1
4 4 5 5 = 2
4 4 5 5 = 3
and so on .......
:-)
You do not need a university degree to handle this game.
Everyone can play. It is meant to exercise your brain, nothing taxing.
What is this game about?
Challenge
There is a series of numbers that you have to add mathematical operators (+, -, / , x or brackets) to. The addition of these operators has to satisfy the end result though.
Example:
2 2 2 2 = 0 => Solution is 2 + 2 - 2 - 2 = 0
2 2 2 2 = 1
2 2 2 2 = 2
2 2 2 2 = 3
2 2 2 2 = 4
2 2 2 2 = 5
2 2 2 2 = 6
2 2 2 2 = 7
2 2 2 2 = 8
2 2 2 2 = 9
Nothing difficult, right? It is just to get your brain moving, otherwise it will go rusty.
Enjoy yourself.
You may also alter the list to include other numbers.
4 4 5 5 = 1
4 4 5 5 = 2
4 4 5 5 = 3
and so on .......
:-)
Sunday, 7 September 2008
Matrices | What is Minor?
Before you read this, say "maths is interesting!". Mental trick....
Now you may start.
In matrices, there is an important basic term residing in it.
It is the term called "minor" and is obtained through the determinant of the matrix.
For 2nd order matrix (or determinant), there will be 4 minors since there are 4 elements within the determinant.
For 3rd order form, there will inevitably, be 9 minors.
To have an idea what "order of matrix" is about, go to this link here.
How to compute this minor?
See below...
The method is simple, right?
It involves the correct cancellation of the appropriate row and column.
The leftover elements will be used to determine the value.
To enhance understanding, let's do another example.Find the minor of element 2.
The leftover is the elements
4 6
7 9
The determinant value of the leftover is then (4)(9) - (7)(6) = 36 - 42 = -6.
This is the minor for element "2".
Common mistake made:
The minor is always taken as the actual element in question.
Example of mistakes:
To find the minor of element "2" in the above determinant
==> Wrong answer = "2", the original element used to get the leftover after cancellation.
To find the minor of element "1" in the above determinant
==> Wrong answer = "1", the original element used to get the leftover after cancellation.
NOTE:
Minor and Co-factor are closely related. They are needed to compute Adjoint and Inverse matrix.
You have to master these concepts to be able to handle matrices.
Tough, right? If your answer is YES, you are wrong!
Look and review the above methods again, and you will be sure that they are simply +, _, x only.
Isn't this what you have been learning since lower elementary?
:-)
Now you may start.
In matrices, there is an important basic term residing in it.
It is the term called "minor" and is obtained through the determinant of the matrix.
For 2nd order matrix (or determinant), there will be 4 minors since there are 4 elements within the determinant.
For 3rd order form, there will inevitably, be 9 minors.
To have an idea what "order of matrix" is about, go to this link here.
How to compute this minor?
See below...
The method is simple, right?
It involves the correct cancellation of the appropriate row and column.
The leftover elements will be used to determine the value.
To enhance understanding, let's do another example.Find the minor of element 2.
The leftover is the elements
4 6
7 9
The determinant value of the leftover is then (4)(9) - (7)(6) = 36 - 42 = -6.
This is the minor for element "2".
Common mistake made:
The minor is always taken as the actual element in question.
Example of mistakes:
To find the minor of element "2" in the above determinant
==> Wrong answer = "2", the original element used to get the leftover after cancellation.
To find the minor of element "1" in the above determinant
==> Wrong answer = "1", the original element used to get the leftover after cancellation.
NOTE:
Minor and Co-factor are closely related. They are needed to compute Adjoint and Inverse matrix.
You have to master these concepts to be able to handle matrices.
Tough, right? If your answer is YES, you are wrong!
Look and review the above methods again, and you will be sure that they are simply +, _, x only.
Isn't this what you have been learning since lower elementary?
:-)
How To Get Determinant Value
In the study of matrices, you will come across the computation of determinant and their values.
These determinants come in various order.
There are the 2nd order, 3rd order, and so on.
What is this order?
Order is the number of rows and column within the determinant.
Thus, 2nd order determinant has 2 rows and 2 columns.
3rd order has 3 rows and 3 columns.
To calculate the values of these determinants, see below for the methods.
The 2nd order is shown in the first upper line.
Following that is the 3rd order computation, using the special Rule of Sarrus (the simpler form of 3rd order calculation).
This value computed comes in useful to determine other values.
One of the examples is the solution of simultaneous equations and their unknowns.
The technique presented here is thus, basic knowledge in matrices learning.
These determinants come in various order.
There are the 2nd order, 3rd order, and so on.
What is this order?
Order is the number of rows and column within the determinant.
Thus, 2nd order determinant has 2 rows and 2 columns.
3rd order has 3 rows and 3 columns.
To calculate the values of these determinants, see below for the methods.
The 2nd order is shown in the first upper line.
Following that is the 3rd order computation, using the special Rule of Sarrus (the simpler form of 3rd order calculation).
This value computed comes in useful to determine other values.
One of the examples is the solution of simultaneous equations and their unknowns.
The technique presented here is thus, basic knowledge in matrices learning.
Saturday, 6 September 2008
Adjoint and Inverse Matrix } Their relationship
There is a common misunderstanding among math learners over the common term in matrices.
The two terms are the Adjoint and Inverse matrix.
The operation to get them is somewhat always confused and "mixed up".
Here to clear and simplify their differences:
- Adjoint matrix
It is obtained through the co-factors of each elements within the matrix. After which the matrix is transposed. It stops there.
- Inverse matrix
The adjoint matrix forms part of this inverse matrix!
Inverse matrix needs a further computation of the determinant also.
The final outcome is the adjoint matrix divided by this determinant value.
Therefore in summary, inverse matrix is formed out of the adjoint matrix.
They are husband and wife, with the kids, the minor and co-factors in them.
.
The two terms are the Adjoint and Inverse matrix.
The operation to get them is somewhat always confused and "mixed up".
Here to clear and simplify their differences:
- Adjoint matrix
It is obtained through the co-factors of each elements within the matrix. After which the matrix is transposed. It stops there.
- Inverse matrix
The adjoint matrix forms part of this inverse matrix!
Inverse matrix needs a further computation of the determinant also.
The final outcome is the adjoint matrix divided by this determinant value.
Therefore in summary, inverse matrix is formed out of the adjoint matrix.
They are husband and wife, with the kids, the minor and co-factors in them.
.
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