Consider x to be an m-by-n array with m n. Which of the following statements is true regarding y = np.zeros(np.size(x))?

Question

Consider x to be an m-by-n array with m > n. Which of the following statements is true regarding y = np.zeros(np.size(x))?

BlackTom AI · Accepted Answer

np.size(x) returns the total number of elements in x (the product of its shape dimensions). For an m-by-n array x, np.size(x) = m * n, so np.zeros(np.size(x)) creates an array of that many zeros.

Relevant knowledge points:
- In NumPy, x.shape is (m, n) and x.size (or np.size(x)) equals m * n.
- Calling np.zeros(k) with a single integer k returns a 1-D array of length k (shape (k,)), commonly described as a 1-by-k vector (row vector-like in loose notation).
- Passing a tuple like np.zeros((m,n)) would create a 2-D m-by-n array; that is not what np.zeros(np.size(x)) does.

Step-by-step reasoning with a concrete example:
1. Let m = 4 and n = 3 for illustration. Then x.shape = (4, 3).
2. Compute p = np.size(x) = 4 * 3 = 12.
3. Call np.zeros(p) i.e. np.zeros(12). NumPy returns an array with shape (12,) — a one-dimensional array containing 12 zeros.
4. Interpreting that in matrix terms, it is a 1-by-p vector (one row, p entries) in the sense of a flat row vector.

Why option f is correct:
- Option f states the output is a 1-by-p vector where p = m * n. That matches np.size(x) = m * n and np.zeros(scalar) producing a 1-D array of that length.

Why the other choices are incorrect:
- a (1-by-m): would require np.zeros(m), not np.zeros(np.size(x)).
- b (n-by-m): would require np.zeros((n,m)) and also reverses dimensions.
- c (1-by-n): would require np.zeros(n).
- d (m-by-m): would require np.zeros((m,m)).
- e (n-by-n): would require np.zeros((n,n)).

Conclusion: The correct statement is f — the output is a 1-by-p vector where p is the product m * n, which matches the provided answer.

Consider x to be an m-by-n array with m > n. Which of the following statements is true regarding y = np.zeros(np.size(x))?单项选择题

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