[Solved] What is the output of this code? import numpy as np from scipy.linalg import inv matrix = np.array([[1, 2], [3, 4]]) inverse_matrix = inv(matrix) print(np.round(inverse_matrix, 2)) | SciPy

SciPy - Linear Algebra (scipy.linalg)

What is the output of this code?

import numpy as np
from scipy.linalg import inv
matrix = np.array([[1, 2], [3, 4]])
inverse_matrix = inv(matrix)
print(np.round(inverse_matrix, 2))

A[[ -2. 1. ] [ 1.5 -0.5]]

B[[ 4. -2. ] [-3. 1. ]]

C[[ 0.25 0.5 ] [ 0.75 1. ]]

D[[ 1.5 -1. ] [-1.5 1. ]]

Step-by-Step Solution

Solution:

Step 1: Calculate determinant of the matrix
Determinant = (1*4) - (2*3) = 4 - 6 = -2 (non-zero, so invertible).
Step 2: Compute inverse using formula
Inverse = (1/det) * [[d, -b], [-c, a]] = (1/-2) * [[4, -2], [-3, 1]] = [[-2, 1], [1.5, -0.5]].
Final Answer:
[[ -2. 1. ] [ 1.5 -0.5]] -> Option A
Quick Check:
Inverse matrix matches [[ -2. 1. ] [ 1.5 -0.5]] [OK]

Quick Trick: Use formula inverse = 1/det * adjugate for 2x2 matrices [OK]

Common Mistakes:

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What is the output of this code?