consider the matrix (in matlab notation) a = [1, a; a, 1] where the value of a gets close to 1, i.e., a = 0.9; 0.99; 0.999, etc. study how it maps the unit circle x, y = ax. in matlab

To study how the matrix a maps the unit circle x^2 + y^2 = 1, you can plot the transformed circle using MATLAB.

Here's the MATLAB code to achieve this:

main.m
% Define the value of 'a'
a = 0.9;

% Generate a set of angle values (theta)
theta = linspace(0, 2*pi, 100);

% Compute the transformed coordinates
x = a * cos(theta);
y = a * sin(theta);

% Plot the transformed circle
plot(x, y);
title('Mapping of Unit Circle');
axis equal;
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You can replace the value of a with other values such as 0.99 or 0.999 to observe how the mapping changes. The plot function is used to display the transformed circle, and axis equal ensures that the axes are scaled equally to maintain the circle's shape.