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

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rakesh05's profile pic

rakesh05 | High School Teacher | (Level 1) Assistant Educator

Posted on

Our given system is


Multiplying the first two matrices we get


    or,  `[[-2x,-x+7,2x+5]][[x],[-1],[2]]=0`

Multiplying the above matrices we get


or,    `[-2x^2+5x+3]=[0]`

as the element 0 can be written in matrix form `[0].`

Comparing the terms we get


Which is a quadratic equation.

Solving the above equation we get

       `x=-1/2`      and `x=3.` Answer.

pramodpandey's profile pic

pramodpandey | College Teacher | (Level 3) Valedictorian

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


`` `[[-2x-2+2,-x+2.0+7,2x+4+1]][[x],[-1],[2]]=[0]`



comparing element in both side of matrix ,we have


`` `2x^2-6x+x-3=0`



either 2x+1=0

or   x-3=0

so x=-1/2 or x=3

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