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Consider the matrix \(E\) where
\begin{align*}
E=\begin{bmatrix}
m & -9 \\
4 & n
\end{bmatrix}
\end{align*}
For the inverse of \(E\) to exist, the values of \(m\) and \(n\), respectively, cannot be
\(C\)
\(\text{Inverse exists}\ \ \Rightarrow\ \ \operatorname{det}\,E \neq 0\)
\(\operatorname{det}\,E=m \times n-(-9 \times 4)=mn+36\)
\(\text {Only option C gives} \ \ mn=-36\)
\(\Rightarrow C\)
Matrix \(V\) is an \(n \times n\) matrix with a determinant equal to 1 .
The product of \(V \times V^{-1}\) will result in
\(A\)
\(\text{Since matrix determinant}\ \neq 0\ \ \Rightarrow\ \ \text{matrix has an inverse}\)
\(\therefore V \times V^{-1} = I\)
\(\Rightarrow A\)
The preferred number of cafes `(x)` and sandwich bars `(y)` in Grandmall’s food court can be determined by solving the following equations written in matrix form.
`[(5, -9),(4, -7)][(x),(y)]=[(7), (6)]`
--- 2 WORK AREA LINES (style=lined) ---
--- 0 WORK AREA LINES (style=lined) ---
`[(text( __), 9),(text( __), text( __)\ )]`
--- 2 WORK AREA LINES (style=lined) ---
`text(the matrix has an inverse)`
a. `text(S) text(ince determinant) = 1 != 0,`
`->\ text(the matrix has an inverse)`
b. `[(-7, 9),(-4, 5)]`
| c. | `[(x), (y)] = [(-7, 9), (-4, 5)][(7), (6)] = [(7),(2)]` |
`:.\ text(Preferred number of sandwich bars) = 2`