# Summary

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

Summary

In this chapter we have acquired the knowledge of

ôñ           Rank of a matrix

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

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

ôñ           ü (A) ãË 0

ôñ           If A is a matrix of order m û n , then ü(A) ãÊ minimum of {m,n}

ôñ           The rank of a zero matrix is ã0ã

ôñ           The rank of a non- singular matrix of order n û n is ãnã

ôñ           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 .

ôñ           Echelon form

A matrix of order m û 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.

ôñ           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 ü ( [A, B] ) = ü ( A) , then the equations are consistent.

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

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

If ü ([A, B] ) ã  ü ( A) then the equations are inconsistent and has no solution.

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

ôñ           In AX = B if |A| ã  0 then the system is consistent and it has unique solution.

ôñ           Cramerãs rule is applicable only when ö ã  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