Question
To solve a determinant equation such as$$\left|\begin{array}{rr}6 & 4 \\-2 & x\end{array}\right|=2$$expand the determinant to obtain$$6 x-(-2)(4)=2$$Then solve to obtain the solution set $\{-1\} .$ Use this method to solve each equation.$$\left|\begin{array}{rr}-0.5 & 2 \\x & x\end{array}\right|=0$$
Step 1
The determinant of a 2x2 matrix is calculated as the product of the elements on the main diagonal minus the product of the elements on the other diagonal. So, we have: $$(-0.5 \cdot x) - (2 \cdot x) = 0$$ Show more…
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To solve a determinant equation such as $$ \left|\begin{array}{rr} 6 & 4 \\ -2 & x \end{array}\right|=2 $$ expand the determinant to obtain $$ 6 x-(-2)(4)=2 $$ Then solve to obtain the solution set $\{-1\} .$ Use this method to solve each equation. $$ \left|\begin{array}{rr} -0.5 & 2 \\ x & x \end{array}\right|=0 $$
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Determinant Solution of Linear Systems
To solve a determinant equation such as $$ \left|\begin{array}{rr} 6 & 4 \\ -2 & x \end{array}\right|=2 $$ expand the determinant to obtain $$ 6 x-(-2)(4)=2 $$ Then solve to obtain the solution set $\{-1\} .$ Use this method to solve each equation. $$ \left|\begin{array}{rrr} 2 x & 1 & -1 \\ 0 & 4 & x \\ 3 & 0 & 2 \end{array}\right|=x $$
To solve a determinant equation such as $$\left|\begin{array}{rr}6 & 4 \\-2 & x\end{array}\right|=2$$ expand the determinant to obtain $$6 x-(-2)(4)=2$$ Then solve to obtain the solution set $\{-1\} .$ Use this method to solve each equation. $$\left|\begin{array}{rrr} 2 x & 1 & -1 \\ 0 & 4 & x \\ 3 & 0 & 2 \end{array}\right|=x$$
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