Question
Download Solution PDFIf \(\rm A=\begin{bmatrix}1&2&3\\\ 3&4&5\\\ 5&6&7\end{bmatrix}\) and \(\rm B=\begin{bmatrix}1&1&1\\\ 2&2&2\\\ 3&3&3\end{bmatrix}\), then det(A + B) = ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
\(\rm A=\begin{bmatrix}1&2&3\\\ 3&4&5\\\ 5&6&7\end{bmatrix}\) and \(\rm B=\begin{bmatrix}1&1&1\\\ 2&2&2\\\ 3&3&3\end{bmatrix}\)
Concept:
Use concept of sum of matrix in which add elements of same places of both matrix .
determinant of matrix is expansion of matrix with respect to any one row or column .
Calculation:
\(\rm A+B=\begin{bmatrix}1&2&3\\\ 3&4&5\\\ 5&6&7\end{bmatrix}+\begin{bmatrix}1&1&1\\\ 2&2&2\\\ 3&3&3\end{bmatrix}\)
\(\rm A+B=\begin{bmatrix}2&3&4\\\ 5&6&7\\\ 8&9&10\end{bmatrix}\)
A + B = 2(60 - 63) - 3(50 - 56 ) + 4(45 - 48)
A + B = - 6 + 18 - 12
A + B = 0
Hence the option (2) is correct.
Last updated on May 26, 2025
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