Need math?

Dude, no path.

Fills us with wrath

Swells us with wreath

Oh! Not to grave

But to grow.

Math, math, math,

Mother of truth

Author of faith

Dude, it's the path.

In depth of doubt

Math keeps us straight.

Work math at home

Strike with warm chime.

## Thursday, December 03, 2015

## Thursday, November 12, 2015

### Determining the Determinant of a 3x3 matrix

**Introduction**

Let us consider the
2x2 matrix given on the left. Its determinant as per the rule given above is AD-BC.

However, look at the
diagram given right. It can be explained as follows.

**Rotation Method**

Rotate left the
second row to one position and then multiply the entries in the respective
columns. Subtract the second column product from that of the first.

This process can be
extended into higher orders also. This
is done by carefully completing all the rotations depending on the number of
rows. Let us see the case of a 3x3 matrix.

At first, rotate left
the second row to one position and third row to two positions. The matrix thus
obtained is given on the right.

Thus we get A= (A1.B2.C3)+(A2.B3.C1)+(A3.B1.C2).

Now we rotate left
the second row to one more position and the third row to two more positions.
The matrix thus obtained is as follows.

Multiply the values
in each column separately and then add the three products. Thus we get B=(A1.B3.C2)+(A2.B1.C3)+(A3.B2.C1).

The determinant of
the 3x3 matrix is then

A-B = (A1.B2.C3+A2.B3.C1+A3.B1.C2)-( A1.B3.C2+A2.B1.C3+A3.B2.C1).

**Cylindrical Rotation Method**

This process is
better understood if we can represent the matrix cylindrically. Consider a
cylinder that has three horizontal sections which can be rotated freely with
respect to a central vertical axis. Entries in the matrix are given on the
exterior of the cylinder.

After the first set
of two types of left rotations, the cylinder looks like what is on the left.

Multiplying the
entries in the columns separately we get

A=(A1.B2.C3)+(A2.B3.C1)+(A3.B1.C2).

After the second set
of two types of left rotations, the cylinder looks like what is on the right.

B = (A1.B3.C2)+(A2.B1.C3)+(A3.B2.C1).

The determinant of
the 3x3 matrix is then

A-B = (A1.B2.C3+A2.B3.C1+A3.B1.C2)-( A1.B3.C2+A2.B1.C3+A3.B2.C1).

**Palm Method**

This can be
visualized in yet another way also.

Let us use the three
central fingers on the left palm to represent a 3x3 matrix.

Instead of the first
set of rotations, multiply the entries from left as indicated by the dark
lines, starting from the diagonal to get the value A.

**Conclusion**

An advantage of the
above mentioned process is the elimination of the repeated use of plus(+) and minus(–)
which is sometimes disturbing for beginners and non-Mathematics students. Can this method be extended to higher order matrices?

Labels:
determinant,
matrix,
matrix multiplication

## Monday, September 07, 2015

### Before I became a Teacher

Before I became a Teacher never I
knew

That sleeping in the class disturbs

The teaching of the teacher.

That talking in the class makes

The teacher shouting in the class.

That not scribbling in the class augments

The degrading of the student.

That correcting the answer scripts
is tougher

Than attempting all the questions.

That questioning the answers is harder

Than answering the questions.

That coming late for the class is
worse

Than not attending the class.

That absenting in the class is worse

Than not joining for the course.

That photocopying is the greatest
insult

That a teacher can ever bear.

That helping a fellow student
learn is

The second greatest insult to a
teacher.

That teaching is the noblest profession

When all your students become teachers.

## Saturday, September 05, 2015

### The Teacher I adore and Fear...

First impression is the best

But he proved me wrong, my trust

By being different, still a good teacher

Never roamed behind us like a preacher

Fills my eyes with few tears

As I give my ears when he is sad and cares

And he sends deep in me shivers

When he is angry and brings in my fears

Still he tries his best to put me in front

Although we never succeed, he didn't grit

Waiting, giving us our needed space

Putting us equally with the race

Also makes me admire his knowledge

Which through his words clearly acknowledges

Am sure greater heights are awaiting

To celebrate his humble lovely teaching

He is my teacher whom I adore

But fears put me back far from his doors

Doors of wisdom that is open to all

Spread even if no inner voice gives a call.

But he proved me wrong, my trust

By being different, still a good teacher

Never roamed behind us like a preacher

Fills my eyes with few tears

As I give my ears when he is sad and cares

And he sends deep in me shivers

When he is angry and brings in my fears

Still he tries his best to put me in front

Although we never succeed, he didn't grit

Waiting, giving us our needed space

Putting us equally with the race

Also makes me admire his knowledge

Which through his words clearly acknowledges

Am sure greater heights are awaiting

To celebrate his humble lovely teaching

He is my teacher whom I adore

But fears put me back far from his doors

Doors of wisdom that is open to all

Spread even if no inner voice gives a call.

*On the height of my self-doubt,**given to me by one of my students unexpectedly on the Teacher's Day of 2015.*
Labels:
Christ University,
kureethara,
Teacher

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