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Kiara is twice as old as Juhi and thrice as old as Udita. The sum of all their ages is 33 years. If k, j and u represent the ages of Kiara, Juhi and Udita respectively, which matrix equation represents the given scenario? |
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Answer» D. k=2j k=3u k + j + u = 33 This eqn is satisfied only in D. Kj, j and u represent the ages of Kiara, Juhi and Udita respectively. Since, Kiara is twice as old as Juhi. \(\therefore\) K = 2j ⇒ k - 2j = 0---(1) Since, Kiara is thrice as old as Udita. \(\therefore\) K = 3u ⇒ k - 3u = 0---(2) Since, sum of their ages is 33 years. Matrix equation which represent all given scenario. (or equation (1), (2) and (3)) is \(\begin{bmatrix}1&-2&0\\1&0&-3\\1&1&1\end{bmatrix}\)\(\begin{bmatrix}k\\j\\u\end{bmatrix}=\begin{bmatrix}0\\0\\3\end{bmatrix}\) or Ax = b, where A = \(\begin{bmatrix}1&-2&0\\1&0&-3\\1&1&1\end{bmatrix}\), x = \(\begin{bmatrix}k\\j\\u\end{bmatrix}\) b = \(\begin{bmatrix}0\\0\\3\end{bmatrix}\) |
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