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Engineering Mathematics
book

Engineering Mathematics

by Babu Ram
June 2009
Intermediate to advanced content levelIntermediate to advanced
1100 pages
42h 22m
English
Pearson India
Content preview from Engineering Mathematics
13.20 RANK OF A MATRIX

Definition 13.86.    A matrix is said to be of rank r if it has at least one non-singular submatrix of order r but has no non-singular submatrix of order more than r.

Rank of a matrix A is denoted by ρ(A).

A matrix is said to be of rank zero if and only if all its elements are zero.

EXAMPLE 13.43

Find the rank of the matrix

 

image

Solution.   The matrix A is of order 3×4. Therefore, ρ(A) ≤ 3. We note that

 

image

 

Therefore, ρ(A) ≠ 3. But, we have submatrix , whose determinant is equal to –2 ≠ 0. Hence, by definition, ρ(A) = 2.

EXAMPLE ...

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Publisher Resources

ISBN: 9789332515611