Determine the value(s) of x such that [[x,2,1]][[-2,-1,2],[-1,0,2],[2,7,1]][[x],[-1],[2]] = 0

Expert Answers
tiburtius eNotes educator| Certified Educator


We need to solve the above equation.

Let's first multiply  `[[-2,-1,2],[-1,0,2],[2,7,1]][[x],[-1],[2]]`.


Now we have scalar product of two vectors.



When we solve this quadratic equation we get

`x_1=1/2` and `x_2=-3`.

Solutions to the equation are `x_1=1/2` and `x_2=-3.`

mlehuzzah eNotes educator| Certified Educator
`[[x,2,1]][[-2,-1,2],[-1,0,2],[2,7,1]][[x],[-1],[2]] = 0` Multiplying the first two matrices, we have: `[[-2x,-x+7,2x+5]] [[x],[-1],[2]]=0` Multiplying these matrices, we have: `[-2x^2 + x - 7 + 4x + 10] =0` Or: `-2x^2 + 5x + 3 = 0` You can solve this by factoring, or using the quadratic formula: `(-2x-1)(x-3)=0` Thus, `x=-1/2` or `x=3`