How to remove rows with zeros in selected columns?

I have a matrix with 1363 rows and 21 columns. The first column is an identifier (1-21). I need to delete all rows that contain all zeroes with the exception of the first column. For example,

a = [ 1 0 5 0 6

2 0 0 0 0

3 3 5 9 12

4 0 0 0 0

5 6 9 1 0]

I want to produce b

b = [ 1 0 5 0 6

3 3 5 9 12

5 6 9 1 0]

Answer 1

[Scott MacKenzie]

There is probably a simpler solution, but this will work...

a = [ 1 0 5 0 6
      2 0 0 0 0
      3 3 5 9 12
      4 0 0 0 0 ]

a = 4×5

1 0 5 0 6 2 0 0 0 0 3 3 5 9 12 4 0 0 0 0

zeroIdx = ~sum(~a(:,2:end) == 0,2);
a(zeroIdx,:) = []

a = 2×5

1 0 5 0 6 3 3 5 9 12