What will be the output shape of the solution vector when solving a sparse linear system Ax = b where A is a 1000x1000 sparse matrix and b is a vector of length 1000?

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SciPy - Sparse Linear Algebra

What will be the output shape of the solution vector when solving a sparse linear system Ax = b where A is a 1000x1000 sparse matrix and b is a vector of length 1000?

A(1000,)

B(1, 1000)

C(1000, 1000)

D(1000, 1)

Step-by-Step Solution

Solution:

Step 1: Understand dimensions of inputs
Matrix A is 1000x1000, vector b has length 1000 (shape (1000,)).
Step 2: Result shape of solving Ax = b
Solution vector x must have shape (1000,) to satisfy multiplication.
Final Answer:
(1000,) -> Option A
Quick Check:
Solution vector shape matches b length [OK]

Quick Trick: Solution vector matches b's length, shape (n,) [OK]

Common Mistakes:

Confusing vector shape with matrix shape
Assuming solution is 2D array
Mixing row and column vector shapes

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What will be the output shape of the solution vector when solving a sparse linear system Ax = b where A is a 1000x1000 sparse matrix and b is a vector of length 1000?

Step 1: Understand dimensions of inputs

Step 2: Result shape of solving Ax = b

Final Answer:

Quick Check:

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Step 2: Result shape of solving `Ax = b`