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mixer [17]
3 years ago
10

For which values of a does ????3a 2a − 6 6a 4a − 12 ???? have an inverse matrix?

Mathematics
1 answer:
likoan [24]3 years ago
7 0

Answer:

The matrix does not have an inverse.

Step-by-step explanation:

A=\begin{bmatrix}3a & 2a-6\\ 6a & 4a-12\end{bmatrix}

det\ A=3a(4a-12)-6a(2a-6)\\\Rightarrow det\ A=12a^2-36a-(12a^2-36a)\\\Rightarrow det\ A=12a^2-36a-12a^2+36a\\\Rightarrow det\ A=0

Since the determinant of the matrix is zero it is called a singular matrix.

Singular matrices do not have an inverse.

Hence, the matrix does not have an inverse.

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