Question

Find the number of ordered pairs $(m, n)$ which satisfy the system\begin{align*} 4(m - n)$.

a. Determinants
b. Matrix inversion
c. System of linear equations
d. Eigenvectors

Answer 1

The system of linear equations 4(m - n) = 0 has an infinite number of ordered pairs $(m, n)$ as solutions, where m and n can take any value.

Step-by-step explanation:

The given system of linear equations is:

4(m - n) = 0

To find the number of ordered pairs $(m, n)$ that satisfy this system, we need to solve the equation for m and n in terms of each other.

First, let's isolate the variable m:

4m - 4n = 0

Next, let's isolate the variable n:

n = (1/4)m

Now we can see that for any value of m, we can find a corresponding value of n by substituting it into the equation above. This means that there are an infinite number of ordered pairs $(m, n)$ that satisfy the system. In other words, the system has an infinite number of solutions.