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# matrix ranks and simultaneous equations watch

1. if you know the rank of a 3x3 matrix, is there a quick way to solve a set of simultaneous equations involving that 3x3 matrix? thanks for the help
2. there sure is, if you have a set of simultaneous equations with 2 variables then use a 2x2 matrix but if you have one with 3 variables use a 3x3 matrix etc. But you need to use the inverse, its not that complicated when you get your head round it, it's difficult to explain over TSR so here's a web link ... http://www.onlinemathlearning.com/si...-matrices.html
3. if i correctly remember what rank means, its the dimension of the image of the matrix, so if you have a rank 2 3 by 3 matrix it means one of the rows/coloumns is a linear combination of the other...

no idea how this helps xD
4. (Original post by inb)
there sure is, if you have a set of simultaneous equations with 2 variables then use a 2x2 matrix but if you have one with 3 variables use a 3x3 matrix etc. But you need to use the inverse, its not that complicated when you get your head round it, it's difficult to explain over TSR so here's a web link ... http://www.onlinemathlearning.com/si...-matrices.html
thanks also, if its asking me to find the general solution to the matrix equation Ax = 0 (with 3x3 matrices), what does this mean?
5. (Original post by wrooru)
thanks also, if its asking me to find the general solution to the matrix equation Ax = 0 (with 3x3 matrices), what does this mean?
if you're talking about ranks i'm guessing it means find the kernal of map represented by the matrix
6. (Original post by Chaoslord)
if you're talking about ranks i'm guessing it means find the kernal of map represented by the matrix
we have not come across kernels. we have been told not to use them. what else could Ax = 0 mean?
7. (Original post by wrooru)
we have not come across kernels. we have been told not to use them. what else could Ax = 0 mean?
if you know what a rank is you should know what a kernal is since you should be doing rank nullity theorem?

the rank is the dimension of the image of f, the nullity is the dimension of the kernal

the kernal is the set of vectors which become the zero vector

so the matrix A is the matrix which transforms vectors, the set Ax=0 denotes the kernal, all vectors which are mapped to the zero vector

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