What is the determinant of the coefficient matrix of the system
–11
–2
0
55
2 answers:
The first two rows of coefficients are identical, so by inspection, the determinant is 0.
Answer:
The determinant of coefficient matrix of the given system is 0.
Step-by-step explanation:
Given system of equation



The coefficient matrix of the system
![\left[\begin{array}{ccc}-1&-1&-1\\-1&-1&-1\\3&2&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%26-1%26-1%5C%5C-1%26-1%26-1%5C%5C3%262%261%5Cend%7Barray%7D%5Cright%5D)
Let A=![\left[\begin{array}{ccc}-1&-1&-1\\-1&-1&-1\\3&2&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%26-1%26-1%5C%5C-1%26-1%26-1%5C%5C3%262%261%5Cend%7Barray%7D%5Cright%5D)
X=![\left[\begin{array}{}x&y&z\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7B%7Dx%26y%26z%5Cend%7Barray%7D%5Cright%5D)
B=![\left[\begin{array}-3 &8&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D-3%20%268%260%5Cend%7Barray%7D%5Cright%5D)
Therefore , we can AX=B
![\left[\begin{array}{ccc}-1&-1&-1\\1&-1&-1\\3&2&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%26-1%26-1%5C%5C1%26-1%26-1%5C%5C3%262%261%5Cend%7Barray%7D%5Cright%5D)
=![\left[\begin{array}{}-3&8&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7B%7D-3%268%260%5Cend%7Barray%7D%5Cright%5D)
The determinant of coefficient matrix of the given system is given by

By using determinant property : when two rowsor two columns are identical then the value of determinant is equal to zero .

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