Given that \(p = \begin{bmatrix} x&4\\3&7\end{bmatrix} Q =\begin{bmatrix} x&3\\1&2x\end{bmatrix}\) and the determinant of \(Q\) is...
FURTHER MATHEMATICS
WAEC 2023
Given that \(p = \begin{bmatrix} x&4\\3&7\end{bmatrix} Q =\begin{bmatrix} x&3\\1&2x\end{bmatrix}\) and the determinant of \(Q\) isthree more than that of \(P\) , find the values of \(x\).
- A. \(-2,\frac{3}{2}\)
- B. \(2,\frac{3}{2}\)
- C. \(-2,-\frac{3}{2}\)
- D. \(2-,\frac{3}{2}\)
Correct Answer: B. \(2,\frac{3}{2}\)
Explanation
\(p = \begin{bmatrix} x&4\\3&7\end{bmatrix}, Q =\begin{bmatrix} x&3\\1&2x\end{bmatrix}\)
\(p = \begin{bmatrix} x&4\\3&7\end{bmatrix}=7x-12, Q =\begin{bmatrix} x&3\\1&2x\end{bmatrix}=2x^2-3\)
|Q| = |P| + 3 (Given)
\(= 2\times2 - 3 = 7x - 12 + 3\)
\(= 2\times2 - 3 - 7x + 12 - 3 = 0\)
\(= 2\times2 - 7x + 6 = 0\)
\(= 2\times2 - 4x - 3x + 6 = 0\)
\(= 2x(x - 2) - 3(x - 2) = 0\)
\(= (x - 2)(2x - 3) = 0\)
\(\therefore x=2,\frac{3}{2}\)
Post an Explanation Or Report an Error
If you see any wrong question or answer, please leave a comment below and we'll take a look. If you doubt why the selected answer is correct or need additional more details? Please drop a comment or Contact us directly. Your email address will not be published. Required fields are marked *