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Question 3

If A=\(\begin{bmatrix}1 & 2\\4 & 2\end{bmatrix}\), then show that |2A| = 4|A|

Answer

The given matrix is

\(u=\begin{bmatrix}1 & 2\\4 & 2\end{bmatrix}\) 

 

So 2A = 2\(\begin{bmatrix}1 & 2\\4 & 2\end{bmatrix}\)

 

          \(= \begin{bmatrix}2 & 4\\8 & 4\end{bmatrix}\)

 

so L.H.S. = |2A| \(= \begin{bmatrix}2 & 4\\8 & 4\end{bmatrix}\)

                 = 2 x 4 - 4 x 8

                = 8 - 32

                 = -24

 

Now, |A| \(= \begin{bmatrix}1 & 2\\4 & 2\end{bmatrix}\)  
= 1 x 2 - 2 x 4
= 2 - 8
= -6
 
So R.H.S. = 4 |A| = 4 x (-6) = -24
 
So L.H.S. = R.H.S.
 

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