Question

If A=diag(-1,-3,2), then |-2A| is equal to: *

Answer 1

Given :   A=diag(-1,-3,2)

To Find : |-2Al

Solution:

A=diag(-1,-3,2)

=> | A |  = - 1 ( - 3 * 2 - 0)  

= 6

| k A|   = kⁿ| A|   where n * n is order of matrix

Hence | - 2 A |  = (-2)³ | A |

= - 8 * 6

= - 48

or

A=diag(-1,-3,2)

=> 2A =  diag(-2,-6,4)

=> - 2A = diag(2,6,-4)

$\left[\begin{array}{ccc}2&0&0\\0&6&0\\0&0&-4\end{array}\right]$

= 2 ( 6 * (- 4) - 0 )

= - 48

Hence  |-2Al  = -48

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