Question

Consider the 4 × 4 matrix
\(M = \begin{pmatrix} 0 & 1 & 2 & 3 \\ 1 & 0 & 1 & 2 \\ 2 & 1 & 0 & 1 \\ 3 & 2 & 1 & 0 \end{pmatrix}\)
If a_i,j denotes the (i, j)^th entry of M^-1 , then a_4,1 equals __________ (rounded off to two decimal places).

Answer 1

Correct Answer: 0.15

To find \( a_{4,1} \), we need to calculate the inverse of the matrix \( M \) and identify the \( (4,1) \)-th entry of \( M^{-1} \). After performing the matrix inversion and extracting the required element, we obtain the value \( a_{4,1} = 1.15 \).