Question

The Japanese mathematician _____ used the same array methods to solve simultaneous equations in $1683$.
$A.\text{ Seki}$
$B.\text{ William Jones}$
$C.\text{ Galileo Galilei}$
$D.\text{ Leonardo Fibonacci}$

Answer 1

Hint: In this question we have to be asked to tell which mathematician used the same array method to solve simultaneous equations in the year $1683$. We will look at what is the same array method and the various ways to solve simultaneous equations. We will also look at the work of other scientists mentioned in the options.

Complete step by step solution:
The same array method mentioned in the question refers to the determinant method of solving simultaneous equations. This method is also called as the elimination method of solving simultaneous equations.
The scientist who put forward the method of solving arrays in the year $1683$ was Seki. For using elimination method to solve simultaneous equations, he created the notation of determinants. Since some of the methods of Seki had inconsistence, Laplace another famous scientist established the Laplace’s formula.
A general simultaneous equation is in the form
$ax+by=p$
$lx+my=q$
Which can be written in the determinant form as:
$\Rightarrow \left| \begin{matrix}
   a & b \\
   l & m \\
\end{matrix} \right|\left| \begin{matrix}
   x \\
   y \\
\end{matrix} \right|=\left| \dfrac{p}{q} \right|$
Now using row or column operations, the variable $m$ is converted to $0$, which results in elimination of a variable and getting the required answer.

So, the correct answer is “Option A”.

Note: It is to be noted that there are other methods to solve simultaneous equations such as using substitution methods. William Jones is the scientist who created the number pi which is $\pi $. Galileo Galilei was a famous astronomer and scientist and Leonardo Fibonacci was a mathematician responsible for creating the Fibonacci series.