Matrix problem

  • Thread starter nokia8650
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  • #1
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Given that AB = BC, and that A is non-singular, prove that B =C.

I dont know how to do matrices in these forums, so where I write a matrix, I mean (a,b,c,d)

Given that A = (3,6,1,2) and B = (1,5,0,1), find a matrix C whose elements are all non zero.

I can easily do the second part of the question. I cannot understand the logic of the second part of the question - we have proved that B=C, how can C now be non equivalent to B?

Thanks
 

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  • #2
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Because the assumption in the first question is that A is non-singular
 
  • #3
Dick
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Given that AB = BC, and that A is non-singular, prove that B =C.

I dont know how to do matrices in these forums, so where I write a matrix, I mean (a,b,c,d)

Given that A = (3,6,1,2) and B = (1,5,0,1), find a matrix C whose elements are all non zero.

I can easily do the second part of the question. I cannot understand the logic of the second part of the question - we have proved that B=C, how can C now be non equivalent to B?

Thanks

I think you mean AB=AC. Like VeeEight said, in the first problem A is assumed to be nonsingular. The matrix you gave for A is the second part is singular. Ax=0 for some nonzero vector x. Use that to construct a C.
 

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