Business Maths and Statistics : Applications of Matrices and Determinants: Summary

**Summary**

In this chapter we have acquired the knowledge of

·
**Rank of a matrix**

The rank of a matrix *A* is the order of the largest non-zero minor of *A*

·
The rank of a matrix A is the order of
the largest non-zero minor of A

·
ρ (*A*) ≥ 0

·
If A is a matrix of order** ***m*** **×** ***n*** **, then** ***ρ*(*A*) ≤** **minimum of** **{*m*,*n*}

·
The rank of a zero matrix is ‘0’

·
The rank of a non- singular matrix of
order** ***n*** **×** ***n*** **is ‘n’

·
**Equivalent Matrices**

Two Matrices *A*
and *B* are said to be equivalent if
one can be obtained from another by a finite number of elementary
transformations and we write it as *A*
~ *B* .

·
**Echelon form**

A matrix of order *m* × *n* is said to be in echelon form if the
row having all its entries zero will lie below the row having non-zero entry.

·
A system of equations is said to be
consistent if it has at least one set of solution.** **Otherwise, it is said to be inconsistent

If** ρ **(** [***A*,** ***B*]** **)** **=** ρ **(** ***A*)** **, then the equations are consistent.

If** ρ **(** [***A*,** ***B*]** **)** **=** ρ **(** ***A*)=** ***n*** **, then the equations are consistent and
have unique** **solution.

If** ρ **(** [***A*,** ***B*]** **)** **=** ρ **(** ***A*)** **<** ***n*** **, then the equations are consistent and
have infinitely** **many solutions.

If ρ (**[**A, B] ) ≠ ρ ( A) then the equations are
inconsistent and has no solution.

·
| adjA| = |A|^{n−1}

·
If |A| = 0 then A is a singular matrix. Otherwise,
A is a non singular matrix.

·
In AX = B if |A| ≠ 0 then the system is consistent
and it has unique solution.

·
Cramer’s rule is applicable only when Δ ≠ 0 .

Tags : Applications of Matrices and Determinants , 12th Business Maths and Statistics : Chapter 1 : Applications of Matrices and Determinants

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12th Business Maths and Statistics : Chapter 1 : Applications of Matrices and Determinants : Summary | Applications of Matrices and Determinants

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