How do I generate a 1*4 unit matrix perpendicular to a random generated 1*4 matrix in MATLAB?

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Let your matrix be [a0 a1 a2 a3][a0 a1 a2 a3], then the following matrices are orthogonal:

[1a0 1a1 −1a2 −1a3][1a0 1a1 −1a2 −1a3]

[1a0 −1a1 −1a2 1a3][1a0 −1a1 −1a2 1a3]

[1a0 −1a1 1a2 −1a3][1a0 −1a1 1a2 −1a3]

This is the generic case with all components nonzero. If one of the components vanishes, say a0=0a0=0, then [b0 0 0 0][b0 0 0 0] is orthogonal to that vector.