Match List - I with List - II.
| List - I | List - II | ||
| (A) | \(A=\begin{bmatrix} 6 & 9\\ 2 & 3 \end{bmatrix}\), \(B=\begin{bmatrix} 2 & 6 & 0\\ 7 & 9 & 8 \end{bmatrix}\), AB will be | (I) | \(\begin{bmatrix} 75 & 117 & 72\\ 35 & 39 & 24 \end{bmatrix}\) |
| (B) | \(P=\begin{bmatrix} 8 & 45 & 30\\ 17 & 19 & 5 \end{bmatrix}\), \(Q=\begin{bmatrix} 67 & 72 & 42\\ 8 & 30 & 19 \end{bmatrix}\), P+Q will be | (II) | \(\begin{bmatrix} 75 & 117 & 72\\ 25 & 39 & 24 \end{bmatrix}\) |
| (C) | \(\begin{bmatrix} 85 & 42 & 69\\ 73 & 42 & 50 \end{bmatrix}-\begin{bmatrix} 10 & -75 & -3\\ 38 & 3 & 26 \end{bmatrix}\) | (III) | \(\begin{bmatrix} 75 & 117 & 72\\ 25 & 49 & 24 \end{bmatrix}\) |
| (D) | \(2\begin{bmatrix} 34 & 36 & 30\\ 12 & 18 & 20 \end{bmatrix}+\begin{bmatrix} 7 & 55 & 12\\ 1 & 13 & -16 \end{bmatrix}\) | (IV) | \(\begin{bmatrix} 75 & 127 & 72\\ 25 & 49 & 24 \end{bmatrix}\) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A) - (II), (B) - (III), (C) - (I), (D) - (IV)
The four matrices in List - II differ only in the entries 35/25, 39/49 and 117/127, so it is enough to find these entries carefully.
(A) By row-by-column multiplication:
\(AB = \begin{bmatrix} 12+63 & 36+81 & 0+72\\ 4+21 & 12+27 & 0+24 \end{bmatrix}\)
\(= \begin{bmatrix} 75 & 117 & 72\\ 25 & 39 & 24 \end{bmatrix}\)
This matches (II).
(B) Adding corresponding entries:
\(P + Q = \begin{bmatrix} 75 & 117 & 72\\ 25 & 49 & 24 \end{bmatrix}\)
This matches (III).
(C) Subtracting corresponding entries:
\(\begin{bmatrix} 85-10 & 42+75 & 69+3\\ 73-38 & 42-3 & 50-26 \end{bmatrix} = \begin{bmatrix} 75 & 117 & 72\\ 35 & 39 & 24 \end{bmatrix}\)
This matches (I).
(D) Doubling the first matrix and adding:
\(\begin{bmatrix} 68 & 72 & 60\\ 24 & 36 & 40 \end{bmatrix} + \begin{bmatrix} 7 & 55 & 12\\ 1 & 13 & -16 \end{bmatrix} = \begin{bmatrix} 75 & 127 & 72\\ 25 & 49 & 24 \end{bmatrix}\)
This matches (IV).
So the matching is (A) - (II), (B) - (III), (C) - (I), (D) - (IV).