Answer:
A
Step-by-step explanation:
The determinant of the coefficient matrix is
[tex]\left|\begin{array}{ccc}3&5&1\\2&1&-1\\1&-3&-4\end{array}\right|=-12-5-6-1-9+40=7.[/tex]
Since the determinant is not zero, the system of these three equations has one unique solution.
Answer:
Choice A is correct.
Step-by-step explanation:
We have given the system.
3x+5y+z = 3,
2x+y-z = 2,
x-3y-4z = 1
We have to choose which statement is true for given system.
We have to find determinant of the given system.
[tex]|\left\begin{array}{ccc}3&5&1\\2&1&-1\\1&-3&-4\end{array}\right|[/tex]
= 3(-4-3)-5(-8+1)+1(-6-1) = 3(-7)-5(-7)+1(-7) = -21+35-7 = 7 ≠ 0
Hence , The system of equations has one unique solution because determinant is not zero.
Choice A is correct.
