Solve for X. [[-4,-2],[2,0]] dot X + [[1,1],[0,-4]] = X dot [[0,1],[1,2]]   X = ??

Expert Answers
rakesh05 eNotes educator| Certified Educator

Here because our matrix `[[-4,-2],[2,0]]`  is 2by2. So our vector X should be    `X=[x_1,x_2]^T` .

Now we see that the `X.[[0,1],[1,2]]`  are not conformable for multiplication.

So in order to find the value of X the multiplication should be same sided i.e. of AX=BX form only then we can find the value of the vector X by comparing similar elements.

pramodpandey | Student

[[-4,-2],[2,0]] dot X + [[1,1],[0,-4]] = X dot [[0,1],[1,2]]

`[[-4,-2],[2,0]].X+[[1,1],[0,-4]]=X.[[0,1],[1,2]]`            (i)


=`[[-2,1],[1,0]]`                                                   (ii)

Post multiply (i) by (ii) ,we have

`[[-4,-2],[2,0]]X[[-2,1],[1,0]]+[[1,1],[0,-4]][[-2,1],[1,0]]=X`        (iii)

Let `X=[[a,b],[c,d]]`

substitute X in (iii) and simplify  we have






solving above system of equations in a,b,c and d. we have