Determinants Matrices Question 157
Question: If $ \begin{bmatrix} 2 & 0 & 7 \\ 0 & 1 & 0 \\ 1 & -2 & 1 \\ \end{bmatrix} \begin{bmatrix} -x & 14x & 7x \\ 0 & 1 & 0 \\ x & -4x & -2x \\ \end{bmatrix} = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{bmatrix} $ then find the value of x
Options:
A) $ \frac{1}{2} $
B) $ \frac{1}{5} $
C) No unique value of ‘x’
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] We have $ \begin{bmatrix} 2 & 0 & 7 \\ 0 & 1 & 0 \\ 1 & -2 & 1 \\ \end{bmatrix} $
$ \begin{bmatrix} -x & 14x & 7x \\ 0 & 1 & 0 \\ x & -4x & -2x \\ \end{bmatrix} = \begin{bmatrix} 5x & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 10x-2 & 5x \\ \end{bmatrix} = $
$ \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{bmatrix} $
$ \Rightarrow x=1/5 $
BETA
