Question

Find the values of \[a,b,c\], and \[d\] in \[\begin{bmatrix}2a+b&a-2b\\5c-d&4c+3d\end{bmatrix}=\begin{bmatrix}4&-3\\11&24\end{bmatrix}.\]

Options

• \[a=1,\ b=2,\ c=4,\ d=3\]

• \[a=1,\ b=2,\ c=3,\ d=4\]

• \[a=3,\ b=4,\ c=1,\ d=2\]

• \[a=2,\ b=1,\ c=4,\ d=3\]

Answer 1

Equating corresponding elements gives four equations: \[2a+b=4\], \[a-2b=-3\], \[5c-d=11\], and \[4c+3d=24\]. Solving them gives \[a=1\], \[b=2\], \[c=3\], and \[d=4\].