After being told that finding the determinant of a four-by-four matrix was so complicated that it should be solved with a computer algorithm, Abhinav Venigalla ’15 discovered a simpler method to find the determinant last Winter Term while in Math 380, accelerated Precalculus.
Venigalla’s solution is now published in the “Reader Response” section of February’s “Mathematics Teacher,” an academic journal that publishes research in the field of mathematics education.
A matrix is a rectangular array of numbers, symbols or expressions arranged in rows and columns. The determinant of a matrix is a mathematical expression that “determines” whether the matrix can be inversed.
The method for finding the inverse of a four-by-four matrix is extremely complicated, according to Patrick Farrell, Chair and Instructor in Math. Farrell told Venigalla’s math class that although they should know how to find the determinant of a four-by-four matrix, they would typically use a calculator or computer to solve it.
After learning about four-by-four matrices in class, Venigalla decided to experiment with finding a new way to find their determinants.
“Mr. Farrell showed us a shortcut to find the determinant of a three-by-three matrix, so I thought there must be a shortcut for the four-by-four as well. So, after class, I tried to find it,” Venigalla said.
“When I solved it, I was kind of surprised. I thought it would be something more complicated, but it actually turned out kind of nice,” Venigalla said.
Venigalla only knew he had found something new when he showed his method to Farrell the next day in class, and Farrell had never seen it before. Farrell urged him to send a letter to the “Reader Response” section of “Mathematics Teacher.”
“I’ve been looking at “Mathematics Teacher” for many, many years, and so whenever I see something that a student has done that’s really interesting, I encourage them to send it into the ‘Reader Reflections,’” Farrell said.
Venigalla re-factored the original expression for the four-by-four matrix to find that it was just six groups of two-by-two matrices. “Using some factoring, however, we can simplify this formula even further to a series of just six products involving determinants of two-by-two matrices within the four-by-four matrix,” reads Venigalla’s letter in the journal.
Farrell helped Venigalla draft the letter to accompany his solution for the journal, but Venigalla created the solution on his own.
Venigalla sent his letter to the journal on January 14, 2012, but the article was not printed until this month because the editors of the magazine had to ensure this method had not been done previously.
“It would be pretty pointless to publish a letter if it was a method that a bunch of people had done before,” said Farrell.
“Mathematics Teacher” informed Venigalla and Farrell in August that the letter would be published in the February edition.
Venigalla, who placed in Math 380 as a Junior, has always had a special curiosity for math.
“To be able to look at something that mathematicians have been doing for over a hundred years and be able to play around with it and see something fall out that, as far as I know, no other mathematician has done before, that’s really special,” said Farrell.
“I think that Andover’s math program is really challenging, especially with Majors [long-term group math projects]. It makes you think more, like not just to ‘rinse and repeat’ the problems, but to think more,” said Venigalla.
Venigalla’s talents in math were evident even in middle school. In eighth grade, Venigalla was featured on CNN for getting a 1590 out of 1600 on the SAT in seventh grade, including a 790 out of 800 on the Math portion.
Additionally, Venigalla earned perfect scores on Florida’s Comprehensive Assessment Test two years in a row and has won both a national math competition and a robotics competition. He surpassed the math offerings at his previous magnet school and began taking online courses, according to the CNN article about Venigalla’s success on the SAT.
“Mathematics Teacher,” the journal in which Venigalla’s work was published, is a publication of the National Council of Teachers of Mathematics. Donald Barry, Instructor in Mathematics, wrote an article on solving an ancient tablet with his Calculus class, which was also published in this journal in 2000.
