Question

The matrix with rank r has

(a) Non zero minor of order r(b) Non zero minor of order greater than r (c) Zero

minor of order r (d) Zero minor of order greater than r​

Answer 1

The matrix with rank r has  Non zero minor of order r

Therefore, option (a) is correct.

Step-by-step explanation:

• Minor of a matrix is determinant of any smaller square matrix obtained after removing one or more rows or cloumns of the matrix

• Rank of matrix is independent number of rows (or columns) in it

• Therefore, any matrix formed by taking all the independent rows and columns must be its submatrix whose order is r

• The determinant of this submatrix will be non zero

• Thus the minor will be non zero with order r

Hope this answer is helpful.

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