Important Formulas and Notes in Applications of Matrices and Determinants

Dear students, before you start revision for each chapter, first make sure you revise all the formulas and key points. Only if you are thorough with the main concepts and formulas, you can confidently work out all the sums. That said, here are the most important formulas in Applications of Matrices and Determinants, Class 12 Business Maths.

You can find links to the other exercises also below.

Examples in Chapter 1 Matrices and Determinants

Text Book Solutions for Exercise 1.1

Text Book Solutions for Exercise 1.2

Text Book Solutions for Exercise 1.3

Text Book Solutions for Exercise 1.4

Important Formulas in Applications of Matrices and Determinants

Rank of a matrix

• The rank of a matrix A is the order of the largest non-zero minor of A.
• 
• If A is a matrix of order m x n, then
• The rank of a zero matrix is 0
• The rank of a non- singular matrix of order n x 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. We write it as .

Echelon form

A matrix of order m x 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.

Consistent Equations

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 , then the equations are consistent.

If , then the equations are consistent and have a unique solution.

If , then the equations are consistent and have infinitely
many solutions.

If , then the equations are in consistent and have no solution.

then A is a singular matrix. Otherwise, A is a non singular matrix.

In AX = B if then the system is consistent and it has unique solution.

Cramer’s rule is applicable only when