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Nullity of a matrix = Total  number columns – Rank of that matrix

But how to calculate value of x when nullity is already given(1 in this case)

in Linear Algebra by Active (1.3k points)
edited by | 145 views

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Nullity of a matrix = Total  number columns – Rank of that matrix = n-r

So n-r = 1 (Given)

Hence r= 3-1 = 2

As rank of matrix is 2, so Determinant of A should be equal to 0.

Hence, |A| = 2*(x-18) - 3*(x-81) + 7*(2-9) = 0

So x = 158.
by Active (4.9k points)
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Thank you so much..

one more doubt

What if they gave n-r=2 ... i.e. r=1
Rank of a matrix being 1 denotes that number of non-zero rows in Echleon form is 1. So in that case, after converting the given matrix to echleon form whereby you will get 2 rows or 2 columns of the transformed matrix as 0, you need to equate whatever element you get regarding x to zero so that the above mentioned condition is satisfied( i.e. getting two rows or two columns as 0 in the transformed matrix).

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