Match List-I with List-II
| List-I | List-II | ||
|---|---|---|---|
| (A) | \(\begin{bmatrix}1&2\end{bmatrix}\begin{bmatrix}3\\4\end{bmatrix}\) | (I) | \(\begin{bmatrix}3\end{bmatrix}\) |
| (B) | \(\begin{bmatrix}2&-1&3\end{bmatrix}\begin{bmatrix}1\\2\\1\end{bmatrix}\) | (II) | \(\begin{bmatrix}8\end{bmatrix}\) |
| (C) | \(\begin{bmatrix}-1&4\end{bmatrix}\begin{bmatrix}5\\3\end{bmatrix}\) | (III) | \(\begin{bmatrix}11\end{bmatrix}\) |
| (D) | \(\begin{bmatrix}3&0&-2\end{bmatrix}\begin{bmatrix}2\\5\\-1\end{bmatrix}\) | (IV) | \(\begin{bmatrix}7\end{bmatrix}\) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A)-(III), (B)-(I), (C)-(IV), (D)-(II)
A row matrix of order \(1 \times n\) times a column matrix of order \(n \times 1\) is a matrix of order \(1 \times 1\); its only element is the sum of the products of corresponding elements.
(A) \(\begin{bmatrix}1&2\end{bmatrix}\begin{bmatrix}3\\4\end{bmatrix}\)
This matches (III) \(\begin{bmatrix}11\end{bmatrix}\).
\(1(3) + 2(4) = 3 + 8 = 11\)
(B) \(\begin{bmatrix}2&-1&3\end{bmatrix}\begin{bmatrix}1\\2\\1\end{bmatrix}\)
This matches (I) \(\begin{bmatrix}3\end{bmatrix}\).
\(2(1) + (-1)(2) + 3(1) = 2 - 2 + 3 = 3\)
(C) \(\begin{bmatrix}-1&4\end{bmatrix}\begin{bmatrix}5\\3\end{bmatrix}\)
This matches (IV) \(\begin{bmatrix}7\end{bmatrix}\).
\((-1)(5) + 4(3) = -5 + 12 = 7\)
(D) \(\begin{bmatrix}3&0&-2\end{bmatrix}\begin{bmatrix}2\\5\\-1\end{bmatrix}\)
This matches (II) \(\begin{bmatrix}8\end{bmatrix}\).
\(3(2) + 0(5) + (-2)(-1) = 6 + 0 + 2 = 8\)