Plus Two Maths Notes Chapter 4 Determinants is part of Plus Two Maths Notes. Here we have given Plus Two Maths Notes Chapter 4 Determinants.
|Text Book||NCERT Based|
|Category||Kerala Plus Two|
Kerala Plus Two Maths Notes Chapter 4 Determinants
Some Properties of Determinants
- Determinant In = I (In – identity matrix of order n)
- If A and B are square matrices of the same order |AB| = |A| |B|
- If A is a square matrix of order n and λ is any scalar. |λ A| = λn |A|
- If A is a non-singular matrix of order n, then |(adj A)| = |A|n-1
- |A| = |AT|
- |An| = |A|n if n is a positive integer.
- The value of a determinant will not be changed.
- if the rows and columns are interchanged.
- lf one row or column is multiplied by a conštant and added to another row or column.
- The value of the determinant is zero if
- Two rows (column) are identical
- Two rows (column) are proportional
- If a row (column) of a determinant is multiplied by a constant, the value of the determinänt becomes that constant times the original value.
- . If the elements of a row (column) of a determinant are the sum of two numbers then the determinant is the sum of two determinants as follows:
- If elements of a row or column are multiplied with co-factors of any other row or column then their sum is zero. For eg: a11 A21 + a12 A22 + a13 A23 = 0
- Consider the system of equations
a1x + b1y + c1z = d1
a2x + b2y + c2z = d2
a3x + b3y + c3z d3 To solve this system of equations using the matrix method,
The above system of equations can be expressed as AX = B, then the solution is given by X = A-1 B.
(i) 1f |A| ≠ 0 the system is consistent and has a unique solution given by X = A-1B
(ii) If |A| = 0 and (adjA)B ≠ 0, the system is inconsistent and has no solution.
(iii) If |A| = 0 and (adj)B = 0, then the sys. tern may be consistent and has infinitely many solutions. In order to find these infinitely many solutions, replace one of the variables by k (say z = k) and solve any two of the given equations for x and y ¡n terms of k.
- Area of a triangle with vertices
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