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The determinant of the matrix $\begin{bmatrix} 6 & -8 & 1 & 1 \\ 0 & 2 & 4 & 6 \\ 0 & 0 & 4 & 8 \\ 0 & 0 & 0 & -1 \end{bmatrix}$

  1. $11$
  2. $-48$
  3. $0$
  4. $-24$
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3 Answers

Best answer
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As the given matrix upper traingular matrix, determinant will be the product of main diagonal elements.

$det(A) = 6*2*4* -1 = -48.$

Similar concept can be appliead, if Matrix is lower triangular or Diagonal Matrix.
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For upper and lower triangular matrix diagonals are the eigenvalues.

The product of all those eigenvalues is equal to the determinant of that matrix.

So it saves time to compute the determinant of the 4*4 matrix.

In this Qs eigenvalues are 6,2,4,-1 and their product is -48 (answer option (B))
Answer:

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