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CMI-2019-DataScience-A: 4

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Let $A=\begin{bmatrix} 1& 1& 1\\0&2&2\\0&0&3 \end{bmatrix}, B=\begin{bmatrix} 5&5&5\\0&10&10\\0&0&15\end{bmatrix}, C=\begin{bmatrix} 3&0&0\\3&6&0\\3&6&9 \end{bmatrix}$. Which of the following statements are true?

  1. $|A|=|B|$
  2. $|B|=125|A|$
  3. $|C|=27|A|$
  4. $|C|=\frac{|A|}{3}$
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For any triangular matrix (upper triangular or lower triangular), the determinant is equal to the product of leading diagonal elements.

Here $A, B$ are upper triangular matrix & $C$ is a lower triangular matrix.

$\therefore |A|=1*2*3=6$

$|B|=5*10*15=750$

$|C|=3*6*9=162$

form the above we can check the options:

  1. option A is false here
  2. option B is true, $750=125*6=750$
  3. option C is also true, $162=27*6=162$
  4. option D is false.

Option B & C is correct.

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