is there any short cut to find the determinant of the matrix

Question

1  0  0  0  0  2

0  1  0  0  2  0

0  0  1  2  0  0

0  0  2  1  0  0

0  2  0  0  1  0

2  0  0   0  0  1

Answer 1

use LU decomposition method .... then this will convert the matrix into a lower triangular matrix. whose determinant (which is also the determinant of original matrix) can be calculated by multiplying the all diagonal elements of the matrix.

Comments

thanku sir

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@suraj
R2 - alpha *R1 ( R2 <- R2 -alpha *R1)
|A'| = |A| + (-alpha) * |B|
|B| = 0
even at this point problem is same i.e. |A| .
could  u explain with example ??
please

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I was saying that |A| and |A'| would be same. You can check it with any matrix.

 

Suppose consider a 2 X 2 matrix, whose determinant value is 2-8 =-6.

      2    1

      8    1

 

Suppose now we perform the following transformation on the given matrix.

R2 <- R2 - 4*R1

then new matrix would be,

  2    1

  0    -3

determinant of this matrix is also same as the determinant of original matrix.