Q1. 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
Q2. A square matrix of order 3 with a non-zero determinant has rank
(a) Less than 3 (b) Equal to 3 (c) One (d) Can’t be determine
Answers
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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.
Know More:
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Step-by-step explanation:
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