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If A=Matrix [(1,0,1),(0,1,2),(0,0,4)] Then Show that `|3a| = 27|A|` - CBSE (Commerce) Class 12 - Mathematics

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Question

if A=`[(1,0,1),(0,1,2),(0,0,4)]` then show that `|3A| = 27|A|`

Solution

The given matrix is A = `[(1,0,1),(0,1,2),(0,0,4)]`

It can be observed that in the first column, two entries are zero. Thus, we expand along the first column (C1) for easier calculation.

From equations (i) and (ii), we have:

|3A|  = 27|A|

Hence, the given result is proved.

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Solution If A=Matrix [(1,0,1),(0,1,2),(0,0,4)] Then Show that `|3a| = 27|A|` Concept: Determinants of Matrix of Order One and Two.
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