Find the inverse begin vmatrix 5 amp 3 6 amp 4 ... - JAMB Mathematics 2013 Question
Find the inverse \(\begin{vmatrix} 5 & 3 \ 6 & 4 \end{vmatrix}\)
A
\(\begin{vmatrix} 2 & -\frac{3}{2} \ -3 & -\frac{5}{2} \end{vmatrix}\)
B
\(\begin{vmatrix} 2 & -\frac{3}{2} \ -3 & \frac{5}{2} \end{vmatrix}\)
C
\(\begin{vmatrix} 2 & \frac{3}{2} \ -3 & \frac{5}{2} \end{vmatrix}\)
D
\(\begin{vmatrix} 2 & \frac{3}{2} \ -3 & \frac{5}{2} \end{vmatrix}\)
correct option: b
Let A = (\begin{pmatrix} 5 & 3 \ 6 & 4 \end{pmatrix})
Then |A| = (\begin{pmatrix} 5 & 3 \ 6 & 4 \end{pmatrix}) = 20 - 18 = 2
Hence A-1 = (\frac{1}{|A|}\begin{pmatrix} 4 & -3 \ -6 & 5 \end{pmatrix})
= (\frac{1}{2}\begin{pmatrix} 4 & -3 \ -6 & 5 \end{pmatrix})
= (\begin{pmatrix} 4 \times 1/2 & -3 \times 1/2 \ -6 \times 1/2 & 5 \times 1/2 \end{pmatrix})
= (\begin{vmatrix} 2 & -\frac{3}{2} \ -3 & \frac{5}{2} \end{vmatrix})
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