Question

4Solve for x given that det5 31det2-4Tха

Answer 1

The value of x is 2

Explanation:

We have the following equation:

`\det \begin{pmatrix}4 & -1 \\ -4 & x\end{pmatrix}=\det \: \begin{pmatrix}5 & 3x \\ 1 & 2\end{pmatrix}`

We solve as follows:

`\begin{gathered} \det \begin{pmatrix}4 & -1 \\ -4 & x\end{pmatrix}=4\cdot x-(-4)\cdot(-1)=4x-4 \\ \det \: \begin{pmatrix}5 & 3x \\ \: 1 & 2\end{pmatrix}=5\cdot2-1\cdot3x=10-3x \\ \text{therefore:} \\ 4x-4=10-3x \\ 4x+3x=10+4 \\ 7x=14 \\ x=(14)/(7) \\ x=2 \end{gathered}`