JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If \( X=\begin{bmatrix}x\\ y\\ z\end{bmatrix} \) is a solution of the system of equations \( AX=B \) where \( adj A=\begin{bmatrix}4&2&2\\ -5&0&5\\ 1&-2&3\end{bmatrix} \) and \( B=\begin{bmatrix}4\\ 0\\ 2\end{bmatrix}, \) then \( |x+y+z| \) is equal to:
- A 3
- B \(\frac{3}{2}\)
- C 1
- D 2
Answer & Solution
Correct Answer
(D) 2
Step-by-step Solution
Detailed explanation
\(X = A ^{-1} B=\left(\frac{\operatorname{adj} A }{| A |}\right) B\) \(= \pm \frac{1}{10}\left(\begin{array}{ccc}4 & 2 & 2 \\ -5 & 0 & 5 \\ 1 & -2 & 3\end{array}\right)\left(\begin{array}{l}4 \\ 0 \\ 2\end{array}\right)\)…
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