Question

If every minor of order ' r ' of a 1 point matrix is zero then P(A)=?^(*)​

Answer 1

The stated condition implies that every minor of order 3 and higher are also 0. Hence the rank of the matrix is 0 or 1 or 2, according as it is a null matrix or it is a nonzero matrix with all 2×2 minors as having 0 value or a nonzero matrix with at least one 2×2 minor with value not equal to 0.

Answer 2

Question:

If every minor of order ‘r’ of a matrix is zero then ρ (A) =?

(a) >r

(b) =r

(c) ≤r

(d) <r

Answer:

The correct answer is option (d) <r.

Step-by-step explanation:

By the definition of ‘Rank of a matrix’

A matrix exists said to have rank ‘r’ if

(i) At least one minor of order r exists non-zero.

(ii) All minors of order r+1 exist zero.

∴ The shown matrix (ii) condition appears to be applied

Therefore, rank of matrix ρ (A) = < r.

The correct answer is option (d) <r.

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