[Solved] What will be the output of the following code?import numpy as np from scipy.linalg import qr A = np.array([[2, 1], [1, 3]]) Q, R = qr(A) print(np.round(R, 2)) | SciPy

SciPy - Linear Algebra (scipy.linalg)

What will be the output of the following code?

import numpy as np
from scipy.linalg import qr
A = np.array([[2, 1], [1, 3]])
Q, R = qr(A)
print(np.round(R, 2))

A[[ -2.24 -1.34] [ 0.00 -2.23]]

B[[ 2.24 2.24] [ 0.00 2.24]]

C[[ 2.24 1.34] [ 0.00 -2.23]]

D[[ 2.24 -1.34] [ 0.00 2.23]]

Step-by-Step Solution

Solution:

Step 1: Compute QR decomposition of matrix A
Matrix A is [[2,1],[1,3]]. QR decomposition yields Q and upper triangular R.
Step 2: Calculate R and round values
R is upper triangular with positive diagonal entries. Rounded R is [[2.24, -1.34],[0.00, 2.23]].
Final Answer:
[[ 2.24 -1.34] [ 0.00 2.23]] -> Option D
Quick Check:
R matrix output matches [[ 2.24 -1.34] [ 0.00 2.23]] [OK]

Quick Trick: R is upper triangular with positive diagonal [OK]

Common Mistakes:

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