Solving a matrix (bidiagonal) in MATLAB

I have a matrix of the following form:

    d1  0  0  0  0   0  0       x1        b1
    a1 d2  0  0  0   0  0       x2        b2
    0  a2  d3 0  0   0  0       x3        b3
    0   0  a3 d4 a4  0  0   *   x4   =    b4
    0   0  0  0  d5  a5 0       x5        b5
    0   0  0  0  0   d6 a6      x6        b6
    0   0  0  0  0   0  d7      x7        b7

I need to write a code to solve this system without forward elimination. I was assuming you could just solve for x7 = b7/d7. Then solve for d6 by setting d6 = b6-a6*x7 = b6-a6*(b7/d7) from our first iteration...then carrying the rest backwards to the first row. However, I am experiencing a block:

1) How to hardcore the confusing differences in indeces

2) How to start from a reverse order down from d7 up to the first equation

3) Moreover, how do I generalize this for any system of n? According to personal readings I am doing for recreation, n is odd.

Can anyone assist me in coding this?

EDIT: The coefficient matrix is A, the x column vector can be denoted as X, and the b column vector can be denoted as B for convenience if needed.

Answer 1

[Andrei Bobrov]

X = A\B