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Determinant

Praveen Varghese Thomas
Updated on 06-Feb-2024 11:56:01

Introduction We studied in the previous classes that the system of two linear equations in two variables namely $\mathrm{a_{1}x\:+\:b_{1}y\:=\:c_{1}\:and\:a_{2}x\:+\:b_{2}y\:=\:c_{2}}$ will have unique solution if $\mathrm{\frac{a_{1}}{b_{1}}\:\neq\:\frac{a_{2}}{b_{2}}\:i.e.\:a_{1}b_{2}\:-\:b_{1}a_{2}\:\neq\:0}$. Thus, $\mathrm{(a_{1}b_{2}\:-\:b_{1}a_{2})}$ is the determining factor for the system of two linear equations. We define $\mathrm{a_{1}b_{2}\:-\:b_{1}a_{2}}$ to be the determinant of the square matrix of order 2. In this tutorial we define the determinant of the square matrix of order 2 and 3 and understand the properties of determinants along with some solved examples. Determinant To every square matrix $\mathrm{A\:=\:[a_{ij}]}$ of order 𝑛, we can associate a real or complex number called ... Read More

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