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#?

1 Answer
Apr 26, 2016

Answer:

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#