iv) A student runs a MATLAB script which produces the following output: >> forma

Question

iv) A student runs a MATLAB script which produces the following output: >> format compact; format rat >A[1 2 -3; -4 1-2; 2 2 -3]; >> a1- [16 -3 -14]; >> a3- [1 0 1]; >> a4= [-1; 16; 10]; >> a5 = [1, -14; -9); >> a1+A ans (A*a2) ans ans ans ans a) Explain how the Matlab script shows that the vector a2 is a row or column of the inverse matrix A-1 of A. Which row or column is it? b) Using the Matlab script or otherwise, find A-1 v) Prove that if an n × n matrix A is invertible and both A and A-1 have only integer entries then det(A) ±1

Explanation / Answer

Solution (a):

In MatLab, to write a column, we use values seperated by semi-colon (;) and to insert row values, we use space.

So a2 = [0; -3; -2] is column.

Solution (b):

In MATLAB, we use inv(A) to calculate inverse of a matrix.

So use following command in in your command window to produce inverse of A,

>>inv(A)

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