Determinants Matrices Question 154
Question: If $ A= \begin{bmatrix} \alpha & 0 \\ 1 & 1 \\ \end{bmatrix} $ and $ B= \begin{bmatrix} 9 & a \\ b & c \\ \end{bmatrix} $ and $ A^{2}=B $ , then the value of a + b + c is
Options:
A) 1 or -1
B) 5 or -1
C) 5 or 1
D) no real values
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] We have $ A^{2}= \begin{bmatrix} \alpha & 0 \\ 1 & 1 \\ \end{bmatrix} \begin{bmatrix} \alpha & 0 \\ 1 & 1 \\ \end{bmatrix} = \begin{bmatrix} {{\alpha }^{2}} & 0 \\ \alpha +1 & 1 \\ \end{bmatrix} = \begin{bmatrix} 9 & a \\ b & c \\ \end{bmatrix} $
$ \Rightarrow $ we get $ {{\alpha }^{2}}=9\Rightarrow \alpha =\pm 3 $ and $ a=0,c=1,b=\alpha +1=3+1=4 $ or $ b=-3+1=-2 $
So $ a+b+c=(0+4+1)=5 $ or $ (0-2+1)=-1 $
BETA
