Question

Given the system of equations, match the following items.

2 x - y = 0 x + y = -3

A. [0 -1

-3 1]

B. [2 0

1 -3]

C. [2 -1

1 1]


x determint
y determint
system determent

Answer 1

Answer:

  A.  x-determinant

  B.  y-determinant

  C.  system determinant

Step-by-step explanation:

The "augmented" matrix for the system is the system coefficient matrix with the constants added as an extra column on the right:

$\left[\begin{array}{cc|c}2&-1&0\\1&1&-3\end{array}\right]$

The x-determinant is the determinant of the system matrix after the x-coefficients have been replaced by the constants:

$\left|\begin{array}{cc}0&-1\\-3&1\end{array}\right|$

The y-determinant is the determinant of the system matrix after the y-coefficients have been replaced by the constants:

$\left|\begin{array}{cc}2&0\\1&-3\end{array}\right|$

Of course, the system determinant is the determinant of the matrix of coefficients of the variables:

$\left|\begin{array}{cc}2&-1\\1&1\end{array}\right|$

_____

Comment on these determinants

Cramer's rule tells you the solution to the system is ...

  x = (x-determinant)/(system determinant)

  y = (y-determinant)/(system determinant)