Question

If A = diag (4, 2, 1) then det A is equal to ……………

Answer 1

Given : A = diag (4, 2, 1)

To Find : det A

Solution:

A = diag (4, 2, 1)

$A=\left[\begin{array}{ccc}4&0&0\\0&2&0\\0&0&1\end{array}\right]$

det A = | A |

| A |  = 4 ( 2 x 1  - 0 x 0 )  - 0 ( 0 x 1  - 0 x 0 )  + 0( 0 x 0 - 0 x 2)

=>| A |  =   4( 2 - 0)  - 0(0 - 0) + 0(0 - 0)

=> | A |  =   4( 2)  - 0(0) + 0(0)

=>  | A |  =   8  - 0  + 0

=>  | A |  =   8

det A   = 8

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