Determinants Class 12 Notes- Chapter 4
Determinants Class 12 Notes- Chapter 4 What is Determinant of a matrix? When a square matrix “A” of an order “n” is associated with a number, then it is titled as a determinant of the aforementioned matrix. The number involved in this square matrix can be a real number or a complex number. Introduction to Determinants Development of determinants took place when mathematicians were trying to solve a system of simultaneous linear equations . E.g.\left. \begin{matrix} {{a}_{1}}x+{{b}_{1}}y={{c}_{1}} \\ {{a}_{2}}x+{{b}_{2}}y={{c}_{2}} \\ \end{matrix} \right] \Rightarrow x=\frac{{{b}_{2}}{{c}_{1}}-{{b}_{1}}{{c}_{2}}}{{{a}_{1}}{{b}_{2}}-{{a}_{2}}{{b}_{1}}}\;\;\; and \;\; y=\frac{{{a}_{1}}{{c}_{2}}-{{a}_{2}}{{c}_{1}}}{{{a}_{1}}{{b}_{2}}-{{a}_{2}}{{b}_{1}}} E . g . a 1 x + b 1 y = c 1 a 2 x + b 2 y = c 2 ] ⇒ x = a 1 b 2 − a 2 b 1 b 2 c 1 − b 1 c 2 a n d y = a 1 b 2 − a 2 b 1 a 1 c 2 − a 2 c 1 Mathematicians defined the sym