When maximizing a function, the gradient at a given point will always point in Notes: In machine learning, when we are trying to learn parameters to solve a problem the direction of the gradient will be crucial to finding "good" parameters! any direction the direction of steppest ascent the direction away from the origin O the direction of steppest descent

Please use matlab

thermostat, which will turn the heat on when the room temperature drops h degrees below its set point, Ts, and cuts heat off at a temperature h degrees higher than Ts . The system heats at a constant rate Q (thermal units per time unit), and the volume of the room is V, so, if the room were perfectly insulated, the heating system would raise the temperature of the room at the rate KVQ (degrees per time unit), where K is a constant of proportionality giving the change in temperature per thermal unit per unit volume. However, there is a heat loss to the outside that is proportional to the difference in temperature between the room and the outside. Using the modified Euler method, write a FORTRAN program to simulate this system, if the room temperature at time is T(t), T(0) = To, and the outside temperature, Tout' is given by: Case (1) : Tout is constant < Ts Case (2) : Tout = A sin(wt + 4)| , %3D reflecting daily cycles. A is temperature range, 2n/w is the period of a cycle, and o is the…

The following is a Matlab code. I am getting too big of an error. The max error should be less than 1*10^-3. I think its because of the backslash operator I used here, X = A \ b. I can't do X = A * inv(b) because b is not a square matrix. How should I reduce the error? % Problem 1% Step 1: Compute the right-hand side vector bn = 20;Xo = ones(n, 1); % Column vector with ones in each componentA = zeros(n); % Initialize the matrix A for i = 1:n   for j = 1:n       A(i, j) = 1 / (i + j - 1);   endend b = A * Xo; % Step 2: Solve the system AX = b numericallyX = A \ b; % Backslash operator for numerical solution % Step 3: Compute the error vector E and find the maximum componentE = X - Xo;E_inf = max(abs(E));