Question

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`?

Answer 1

Determinant of is `M+N=69` and that of `MXN=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 `2xx2` matrix.

`M+N=[(-1,2),(-3,-5)]`+`[(-6,4),(2,-4)]`=`[(-7,6),(-1,-9)]`

Hence its determinant is `(-7xx-9)-(-1xx6)=63+6=69`

`MXN=[(((-1)xx(-6)+2xx2),((-1)xx4+2xx(-4))),(((-1)xx2+(-3)xx(-4)),((-3)xx4+(-5)xx(-4)))]`

= `[(10,-12),(10,8)]`

Hence deeminant of `MXN=(10xx8-(-12)xx10)=200`