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 ai,j denotes the (i, j)th entry of M-1 , then a4,1 equals __________ (rounded off to two decimal places).
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 ai,j denotes the (i, j)th entry of M-1 , then a4,1 equals __________ (rounded off to two decimal places).
\(M = \begin{pmatrix} 0 & 1 & 2 & 3 \\ 1 & 0 & 1 & 2 \\ 2 & 1 & 0 & 1 \\ 3 & 2 & 1 & 0 \end{pmatrix}\)
If ai,j denotes the (i, j)th entry of M-1 , then a4,1 equals __________ (rounded off to two decimal places).
Updated On: Jan 25, 2025
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Correct Answer: 0.15
Solution and Explanation
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 \( a_{4,1} = 1.15 \).
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