Last two years were my hectic journey of academic life which was so hard however it was paid off. Finally, I achieved my another Master Degree (MSc) in food security and development from the University of Reading, United Kingdom. The strong knowledge of food security has widened my future responsibility in chasing the solution of malnutrition, […]
Dogs and me have a very cordial relationship since my childhood. They trust me and I trust them. With cats it has been on and off, some have been best of friends while some would want to send me to the moon. Right or wrong my conviction is that mostly when you treat an animal well, it will treat you well too.
I believe if evey institute had one or two institute pets, it would go a long way reducing exam stress in the students and help them bond better.
I would not mind supporting a pet, would you?
It is the time of exam again and there is the usual stream of students asking for
clarification and solution of different concepts. So here I discuss some common doubts.
Chapter 2: problem 2: Definition of a line passing through the origin in various ways.
(1) is useful only in two dimensions.
(2) Defining a line as collection of position vectors given by , where can be a vector in any dimensions and . For example with would define the x-axis in three dimensions.
(3) Defining a line as intersection of two planes in 3 dimensions, for example the
intersection of the xy-plane and the xz-plane defines the x-axis.
Given any two equations of planes passing through zero, one can find the intersection and express it in terms of scaling of a vector. As an example, the intersection of and requires that , and substituting these conditions for the coordinates of a general point gives The equation of a general line (not necessarily passing through the origin) can be written as where is a constant vector.
Chapter 2: problem 4, how to find a plane that passes through the given three points. Assume a general equation of a plane , insist that the given points satisfy the equation and solve for .
Chapter 3: problem 5, notice that the B matrix has only two rows that are linearly independent. There are 3 variables, hence one variable is free. Thus either there are infinite solutions or there is no solution. When the is chosen such that equations 1 and 3 and equations 2 and 4 are the same, the equation is solvable with infinite solutions, whereas if is chosen so that two of there equations are different then the matrix equation has no solution.
I have been experimenting with giving engineering students a wider flavor of possible projects that they can take over using linear algebra and coding. Towards this directions we did the following activities.
(1) A session on reading an introductory article on chemometrics, followed by a quiz. The reading was open network where students were encouraged to find references and understand notations used. I gave a brief introduction and then let them figure out some of the technicalities for the quiz.
(2) A mechanical engineering colleague, Dr. Oza and a chemical engineering colleague Dr. Rabari talked to the students about various applications.
I hope to do more intense work with student projects this year. Your comments and insights are welcome.