title: Calculating vector x using backward substitution for upper triangular matrix given matrix 'a' and matrix 'b'
body: <p>According to the pdf mentioned in below link, i need to calculate matrix 'x' given matrix 'A' and<br>
  matrix 'b' for upper triangular matrix using backward substitution.</p>
  
  <p><strong>link: <a href="http://www.mathcs.emory.edu/~haber/math315/chap3.pdf" rel="nofollow">http://www.mathcs.emory.edu/~haber/math315/chap3.pdf</a></strong></p>
  
  <p>Actually i need to use 1 dimensional array only. I have also developed logic for it and tried to<br>
  compile it, but actually it is having few errors of 'expression' and 'initialization'
      |1  2  3|     |x0|      |b0|
      |0  4  5|  x  |x1|  =   |b1|
      |0  0  6|     |x2|      |b2|
  equations:<br>
      1) 6*x2 = b2
      2) 4*x1 + 5*x2 = b1
      3) 1*x0 + 2*x1 + 3*x3 = b0</p>
  
  <hr>
  
  <pre><code>This is my code:
  //here: 's' is size of matrix eg: for 3x3 it is 3
  //x[] i need to get the result
  //b[] it is to be multiplied with cm to get 
  //cm[] is the matrix which will be multiplied with b[] to get x[]
  
      for(int p=s-1; p&gt;0; p--)
          { 
          if(p==s-1)
              {
              x[p] = b[p]/cm[s*s];                        // computing x2
              }
          else
          {
                  for(int j=0; int k=s-p; j&lt;s-i; k&gt;0; j++; k--)
                      {
                          c[p]+ = cm[s*p - j]*x[p+k];
                  }
              }
  
          x[p] = (b[p] - c[p])/cm[s*p-(s-i)];
          }
  Errors: 
  1) variable 'x' may not be initialized
  2) variable 'c' may not be initialized
  3) expression for(int j=10; intk=s-p;j&lt;s-i;k&gt;0;j++;k--) has no effect
  4) expected a ")" in point 3.
  5) expected an expression in line  c[p]+ = cm[s*p - j]*x[p+k];
  6) variable 'x' was set but never used
  
  Please help me how to solve these errors?
  Also let me know is my logic correct?
  </code></pre>