If \(\begin{bmatrix}b & 2b-c \\ d-3c & 5a-d\end{bmatrix}=\begin{bmatrix}4 & 7 \\ 5 & 12\end{bmatrix}\), then the values of a, b, c, d are
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → a = 4, b = 4, c = 1, d = 8
Equal matrices have equal corresponding entries:
\(b = 4\)
\(2b-c = 7 \ \Rightarrow\ c = 8-7 = 1\)
\(d-3c = 5 \ \Rightarrow\ d = 5+3 = 8\)
\(5a-d = 12 \ \Rightarrow\ 5a = 20,\ a = 4\)