Determinants Matrices Question 137
Question: The matrix $ A= \begin{bmatrix} 1 & 3 & 2 \\ 1 & x-1 & 1 \\ 2 & 7 & x-3 \\ \end{bmatrix} $ will have inverse for every real number x except for
Options:
A) $ x=\frac{11\pm \sqrt{5}}{2} $
B) $ x=\frac{9\pm \sqrt{5}}{2} $
C) $ x=\frac{11\pm \sqrt{3}}{2} $
D) $ x=\frac{9\pm \sqrt{3}}{2} $
Show Answer
Answer:
Correct Answer: A
Solution:
- [a] $ A= \begin{bmatrix} 1 & 3 & 2 \\ 1 & x-1 & 1 \\ 2 & 7 & x-3 \\ \end{bmatrix} $
$ | A |=1[(x-1)(x-3)-7]-3[(x-3)-2] $
$ +2[7-2(x-1)] $
$ =x^{2}-11x+29 $ If inverse will not exist then $ | A |=0 $
$ x^{2}-11x+29=0 $
$ x=\frac{11\pm \sqrt{5}}{2} $
BETA
