# Let [(x_(11),x_(12)), (x_21,x_22) ] be defined as an object called matrix. The determinant of of a matrix is defined as [(x_(11)xxx_(22))-(x_21,x_12)]. Now if M[(-1,2), (-3,-5)] and N =[(-6,4), (2,-4)] what is the determinant of M+N & MxxN?

Apr 26, 2016

Determinant of is $M + N = 69$ and that of $M X N = 200$ko

#### Explanation:

One needs to define sum and product of matrices too. But it is assumed here that they are just as defined in text books for $2 \times 2$ matrix.

$M + N = \left[\begin{matrix}- 1 & 2 \\ - 3 & - 5\end{matrix}\right]$+$\left[\begin{matrix}- 6 & 4 \\ 2 & - 4\end{matrix}\right]$=$\left[\begin{matrix}- 7 & 6 \\ - 1 & - 9\end{matrix}\right]$

Hence its determinant is $\left(- 7 \times - 9\right) - \left(- 1 \times 6\right) = 63 + 6 = 69$

$M X N = \left[\begin{matrix}\begin{matrix}\left(- 1\right) \times \left(- 6\right) + 2 \times 2 \\ \left(- 1\right) \times 4 + 2 \times \left(- 4\right)\end{matrix} \\ \begin{matrix}\left(- 1\right) \times 2 + \left(- 3\right) \times \left(- 4\right) \\ \left(- 3\right) \times 4 + \left(- 5\right) \times \left(- 4\right)\end{matrix}\end{matrix}\right]$

= $\left[\begin{matrix}10 & - 12 \\ 10 & 8\end{matrix}\right]$

Hence deeminant of $M X N = \left(10 \times 8 - \left(- 12\right) \times 10\right) = 200$