SOLUTION: Hi please help :) Determine the value(s) of x such that: A= [x,2,1] B= [2,4,-2] [4,1,3] [-2,41,3] C= [x] [-1] [3] So the actual question becomes A*B*C=0 and i need to

Algebra ->  Matrices-and-determiminant -> SOLUTION: Hi please help :) Determine the value(s) of x such that: A= [x,2,1] B= [2,4,-2] [4,1,3] [-2,41,3] C= [x] [-1] [3] So the actual question becomes A*B*C=0 and i need to       Log On


   

Question 1159497: Hi please help :)
Determine the value(s) of x such that:
A=
[x,2,1]
B=
[2,4,-2]
[4,1,3]
[-2,41,3]
C=
[x]
[-1]
[3]
So the actual question becomes A*B*C=0 and i need to determine the value(s) of x Thanks so much
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Multiple matrix multiplications are performed in order, left to right:
A*B*C = (A*B)*C

A*B: (the product of a 1X3 matrix and a 3X3 matrix is a 1X3 matrix)

=
= %28matrix%281%2C3%2C2x%2B6%2C4x%2B43%2C-2x%2B9%29%29

(A*B)*C: (the product of a 1X3 matrix and a 3X1 matrix is a 1X1 matrix)
%28matrix%281%2C3%2C2x%2B6%2C4x%2B43%2C-2x%2B9%29%29%2A%28matrix%283%2C1%2Cx%2C-1%2C3%29%29
= %28matrix%281%2C1%2C%282x%2B6%29%28x%29%2B%284x%2B43%29%28-1%29%2B%28-2x%2B9%29%283%29%29%29
= %28matrix%281%2C1%2C2x%5E2-4x-16%29%29

We need the product of the matrices to be 0:

2x%5E2-4x-16+=+0
x%5E2-2x-8+=+0
%28x-4%29%28x%2B2%29+=+0
x+=+4 OR x+=+-2