Applications of Matrices and Determinants — Chapter Summary
ICSE · Class 12 · Mathematics
Summary of Applications of Matrices and Determinants for ICSE Class 12 Mathematics. Part of the ICSE Class 12 Mathematics syllabus.
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Overview
Applications of matrices and determinants connect algebra with solving linear systems and coordinate geometry. The central ideas are the classification of systems of linear equations as consistent, inconsistent, dependent, or independent, the Matrix Method for solving systems with a unique solution,
Key Concepts
A system of three linear equations
A system of three linear equations in three variables can be written as AX = B, where A is the coefficient matrix, X is the column matrix of variables
A solution is a set
A solution is a set of values of x, y, and z that simultaneously satisfy all the equations of the system.
A system is consistent if it
A system is consistent if it has one or more solutions. A consistent system may have exactly one solution or infinitely many solutions.
A system is inconsistent if it
A system is inconsistent if it has no solution.
A system AX = B
A system AX = B is non-homogeneous if B is not the zero matrix, and homogeneous if B is the zero matrix. Every homogeneous system is consistent becaus
Learning Objectives
- Represent a system of linear equations in matrix form AX = B
- Identify coefficient matrix, variable matrix, and constant matrix
- Classify systems of equations as consistent, inconsistent, dependent, or independent
- Use the determinant of the coefficient matrix to test whether a system has a unique solution
- Apply the condition involving adj A when |A| = 0
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