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### Coursera machine learning week 2 Quiz answer Octave and Matlab Tutorial | Andrew NG￼

1. Suppose I first execute the following Octave/Matlab commands:

A = [1 2; 3 4; 5 6]; B = [1 2 3; 4 5 6];

Which of the following are then valid commands? Check all that apply. (Hint: A’ denotes the transpose of A.)

2. Let

Which of the following indexing expressions gives

Check all that apply.

- B = A(:, 1:2);
- B = A(1:4, 1:2);
- B = A(:, 0:2);
- B = A(0:4, 0:2);

3. Let A be a 10×10 matrix and x be a 10-element vector. Your friend wants to compute the product Ax and writes the following code:

v = zeros(10, 1); for i = 1:10 for j = 1:10 v(i) = v(i) + A(i, j) * x(j); end end

How would you vectorize this code to run without any for loops? Check all that apply.

- v = A * x;
- v = Ax;
- v = x’ * A;
- v = sum (A * x);

4. Say you have two column vectors v and w, each with 7 elements (i.e., they have dimensions 7×1). Consider the following code:

z = 0; for i = 1:7 z = z + v(i) * w(i) end

Which of the following vectorizations correctly compute z? Check all that apply.

- z = sum (v .* w);
- z = w’ * v;
- z = v * w’;
- z = w * v’;

5. In Octave/Matlab, many functions work on single numbers, vectors, and matrices. For example, the sin function when applied to a matrix will return a new matrix with the sin of each element. But you have to be careful, as certain functions have different behavior. Suppose you have an 7×7 matrix X. You want to compute the log of every element, the square of every element, add 1 to every element, and divide every element by 4. You will store the results in four matrices, A, B, C, D. One way to do so is the following code:

for i = 1:7 for j = 1:7 A(i, j) = log(X(i, j)); B(i, j) = X(i, j) ^ 2; C(i, j) = X(i, j) + 1; D(i, j) = X(i, j) / 4; end end

Which of the following correctly compute A, B, C or D? Check all that apply.

- C = X + 1;
- D = X / 4;
- A = log (X);
- B = X ^ 2;

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