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

`[[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`
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`[[x,2,1]][[-2,-1,2],[-1,0,2],[2,7,1]][[x],[-1],[2]]=0`

We need to solve the above equation.

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

`[[x,2,1]][[-2x+5],[-x+4],[2x-5]]=0`

Now we have scalar product of two vectors.

`-2x^2+5x-2x+8+2x-5=0`

`-2x^2+5x+3=0`

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.`

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