Without calculating the determinant, inspect the following:
(7,1) 1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 −2
(7.2) 1 0 0 0
0 1 0 0
0 0 0 1
0 0 1/4 0
(7.1)
Since it is a diagonal matrix.
So, the determinant can be calculated by inspection(by multiplying the diagonal elements)
(7.2)
Interchanging third and fourth row , which is a valid transformation with respect to the determinant (it will leave it unchanged), you will get:
Since it is a diagonal matrix.
So, the determinant can be calculated by inspection(by multiplying the diagonal elements)
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