Question

Which matrix represents the system of equations shown below? y = 5 4x = 3

Answer 1

Answer:

$\left[\begin{array}{ccc}1&0\\0&4\end{array}\right]$ $\left[\begin{array}{ccc}x\\y\end{array}\right]$ = $\left[\begin{array}{ccc}5\\3\end{array}\right]$

Step-by-step explanation:

A matrix is an algorithm that has many applications. It is composed of a series of numbers (typically coefficients of variables) organized in a pattern. When dealing with a matrix, one must always remember the rule (rows by columns). One such application is that a matrix can facilitate the process by which one solves a system of equations.

When given the following system:

y = 5

4x = 3

One can see that not all of the equations have all variables in them. Yet, bear in mind that any number times zero is zero, therefore, one can rewrite the equation such that it has all of the variables if one ensures that the coefficient of the missing variable is (0).

y + 0x = 5

0y + 4x = 3

Now organize this in the form of a matrix, the coefficients of the variable go in a (4 x 4) since there are now (4) elements. The variables are vertically arranged in a (2 x 1), and the equation results are also vertically arranged in a (2 x 1).

$\left[\begin{array}{ccc}1&0\\0&4\end{array}\right]$ $\left[\begin{array}{ccc}x\\y\end{array}\right]$ = $\left[\begin{array}{ccc}5\\3\end{array}\right]$