Discussion
If \(X = A^{-1}B\),Where \(A = \begin{bmatrix} 1 & -1 \\ 2 & 1 \end{bmatrix}\), \(B = \begin{bmatrix} 3 \\ 6 \end{bmatrix}\) and \(X = \begin{bmatrix} x_{1} \\ x_{2} \end{bmatrix}\),then \(x_{1} + x_{2}\) =
Answer: A
\(x_{1} + x_{2} =\) 3.
\(X = A^{-1}B\) means \(AX = B\), that is \(x_{1} - x_{2} = 3\) and \(2x_{1} + x_{2} = 6\). Adding the equations:
\[ 3x_{1} = 9 \;\Rightarrow\; x_{1} = 3,\quad x_{2} = 0 \]
so \(x_{1} + x_{2} = 3\). (The same comes from \(A^{-1} = \frac{1}{3}\begin{bmatrix} 1 & 1 \\ -2 & 1 \end{bmatrix}\).) Values such as 6 or 9 come from multiplying by \(A\) instead of \(A^{-1}\).
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development