Question

How do you evaluate a matrix.

Answer 1

Step 1: Matrix

For evaluating a matrix, it must be a square matrix of order $n\times n$. it can be $2\times 2,3\times 3,4\times 4$

For eg:

${\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]}_{2\times 2}$ is a square matrix of order $2\times 2$

${\left[\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right]}_{3\times 3}$is a square matrix of order $3\times 3$

Step 2: Evaluating a matrix

$A={\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]}_{2\times 2}$we can evaluate the $2\times 2$ matrix by multiplying the and then subtracting it

$\left|A\right|=\left|ad-bc\right|$

For $3\times 3matrix$

Hide row and column along which we evaluating the matrix

Then the remaining element is $\left[\begin{array}{cc}e& f\\ h& i\end{array}\right]then\left|\begin{array}{c}A\end{array}\right|=\left|\begin{array}{c}ei-fh\end{array}\right|$in this we evaluate the matrix along element $a$.

Similarly, if we evaluate the matrix along element $b$ then $\left|\begin{array}{c}A\end{array}\right|=\left[\begin{array}{cc}d& f\\ g& i\end{array}\right]then\left|\begin{array}{c}A\end{array}\right|=\left|\begin{array}{c}di-gf\end{array}\right|$

Hence, in this way we can evaluate a square matrix .