Match List-I with List-II
| List-I | List-II | ||
| (Matrix) | (Determinant) | ||
| (A) | \(\begin{bmatrix}1 & 7\\-3 & 5\end{bmatrix}\) | (I) | 24 |
| (B) | \(\begin{bmatrix}-2 & 5\\-3 & -3\end{bmatrix}\) | (II) | 32 |
| (C) | \(\begin{bmatrix}-12 & 8\\-16 & 8\end{bmatrix}\) | (III) | 21 |
| (D) | \(\begin{bmatrix}15 & 9\\-21 & -11\end{bmatrix}\) | (IV) | 26 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A)-(IV), (B)-(III), (C)-(II), (D)-(I)
For a 2 × 2 determinant,
\( \displaystyle \begin{vmatrix}a & b\\c & d\end{vmatrix} = ad - bc \)
(A) \(\begin{bmatrix}1 & 7\\-3 & 5\end{bmatrix}\)
\(1(5) - 7(-3) = 5 + 21 = 26\)
This matches (IV).
(B) \(\begin{bmatrix}-2 & 5\\-3 & -3\end{bmatrix}\)
\((-2)(-3) - 5(-3) = 6 + 15 = 21\)
This matches (III).
(C) \(\begin{bmatrix}-12 & 8\\-16 & 8\end{bmatrix}\)
\((-12)(8) - 8(-16) = -96 + 128 = 32\)
This matches (II).
(D) \(\begin{bmatrix}15 & 9\\-21 & -11\end{bmatrix}\)
\(15(-11) - 9(-21) = -165 + 189 = 24\)
This matches (I).
So the matching is (A)-(IV), (B)-(III), (C)-(II), (D)-(I).