Class 12 Math Chapter 4 Determinants Notes(Handwritten Notes)

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Determinants Handwritten Notes PDF

Chapter 3: Matrices
Chapter 5: Continuity and Differentiability

Other Subjects:
Class 12 Physics Notes PDF
Class 12 Chemistry Notes PDF

Key Points

Determinants

Determinant: Determinant is the numerical value of the square matrix. So, to every square matrix A = [a_ij] of order n, we can associate a number (real or complex) called determinant of square matrix A.

This denoted by det A or |A|.

NOTE: Read |A| as determinant A not absolute value of A. Determinant gives numerical value but matrix do not give numerical value.

Only square matrix have determinants.

Solution of system of linear equation using inverse of a Matrix.

Consider the system of equations:

$a₁x + b₁y + c₁z = d₁

a₂x + b₂y + c₂z = d₂

a₃x + b₃y + c₃z = d₃

Then, the system can be written as AX = B

Case 1: If A is a non-singular matrix, then its inverse exists.

X = A^-1B

This matrix equation provides unique solution for the given system of equations as inverse of a matrix is unique.

Case 2: If A is a singular matrix, then |A| = 0.

In this case, we calculate (adjA)B.

If (adjA)B = O, (O being zero matrix), then solution does not exist and the system of equations is called inconsistent.

If (adjA)B = O, then system may be either consistent or inconsistent according as the system have either infinitely many solutions or no solution.

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Summary