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plz give a detailed answer. leave the calculation just explain how to solve it. thankx.

plz give a detailed answer. leave the calculation just explain how to solve it. thankx.

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Grade:12th pass

1 Answers

Latika Leekha
askIITians Faculty 165 Points
6 years ago
Hello student
First of all it is important to be well versed with the concept of rank of a matrix. By definition:
A number ‘r’ is called the rank of an m x n matrix if:
1. Every square sub-matrix of order (r+1) or more is singular and
2. There exists at least one square sub-matrix of order r which is non-singular.
Hence, here since it is given that the rank of the matrix is 1, this means there does not exist any non-singular square sub-matrix of order more than 1. Hence, using this we have that the value of the 2x2 determinant must be zero, i.e.
\begin{vmatrix} -4 & a-4\\ -2& a+1 \end{vmatrix} = 0
This gives a = -6.
Hence, the correct option is (c).

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