Write a library Matrix that implements the following API:

Mathematicians and scientists use mature libraries or special-purpose matrix-processing languages for such tasks. See the booksite for details on using such libraries.

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public class Matrix double dot (double [] a, double[] b) double [] [] double [] [] multiply(double [] [] a, double [] [] b) transpose (double [] [] a) double [] multiply(double [] [] a, double [] x) multiply(double[] x, double [] [] a) double [] vector dot product matrix-matrix product transpose matrix-vector product vector-matrix product