Saved Bookmarks
| 1. |
If \( A \) is a non-singular matrix and \[ (5 A )^{-1}=\frac{1}{\left(n^{2}-n-7\right)} A ^{-1} \text {, } \] then the sum of all possible values of \( n \) is |
|
Answer» A is non singular matrix ∴ |A| \(\ne\) 0 and A-1 will exist. Given that \((5A)^{-1} = \frac{1}{n^2 - n - 7}A^{-1}\) ⇒ \(\frac{A^{-1}}{5} = \frac{A^{-1}}{n^2 - n - 7} \) \(\left(\because (kA)^{-1} = \frac{A^{-1}}{k}\right) \) ⇒ \(n^2 - n - 7 = 5\) ⇒ \(n^2 - n-12 = 0\) ∴ Sum of all possible vowels of \(n=\frac{-b}a= \frac{-(-1)}{1}= 1\). |
|