Help in solving augmented matrix?

Question

Hi,

I am a student of telecom engineering and i am right now facing a problem in solving this linear algebra question. Any help would be highly appreciated.

.............0...................3 -5

Let u = [ 4 ] and A = [ -2 6 ].

.............4...................1 1

Is u in the plane R3.

Please note that the square brackets will be bigger, since here i cant put them bigger.

Kindly i need slution of this question.

Thanks in advance.

Answer 1

I think what you're really asking is this...

Given u, and A as above, find a solution to the equation

u = A x

Is that right?

This is an overdetermined system, so it is not guaranteed to have any solutions at all.  Fortunately for us, this one actually does have a solution.  Here it is:

x = [ 2.5 ]

......[ 1.5 ]

Here is how solved it:  I simplified the equation by removing one row from each of the matrices.  That left me with a simplified equation that must have one solution:

[ 0 ] ... [ 3 -5 ]

[ 4 ] = [ -2 6 ] x

To solve the simplified problem, I calculated the inverse of the 2x2 matrix and multiplied it by the 2x1 matrix.  That gave me a 2x1 value for x.

Then, I needed to check to see if this solution is also a solution of the original problem.  I tried it out, and yes!  It is a (unique) solution to the original problem.