Find the value of x for which the determinant of the matrix is equal to 0: | x-3 x+1 | | x x+2 | = 0
Understand the Problem
The question asks to find the value of $x$ for which the determinant of the given 2x2 matrix is equal to zero. We need to calculate the determinant and set it equal to zero, then solve for $x$.
Answer
$x = -3$
Answer for screen readers
$x = -3$
Steps to Solve
- Calculate the determinant
To find the determinant of a 2x2 matrix $ \begin{vmatrix} a & b \ c & d \end{vmatrix} $, we calculate $ad - bc$. In our case, the determinant is $(x-3)(x+2) - (x+1)(x)$.
- Set the determinant equal to zero
We have the equation $(x-3)(x+2) - (x+1)(x) = 0$.
- Expand the equation
Expanding the terms, we get: $x^2 - 3x + 2x - 6 - (x^2 + x) = 0$ $x^2 - x - 6 - x^2 - x = 0$.
- Simplify the equation
Combining like terms, we get: $-2x - 6 = 0$.
- Solve for x
Adding 6 to both sides: $-2x = 6$ Dividing by -2: $x = -3$.
$x = -3$
More Information
The determinant of the matrix is zero when $x = -3$.
Tips
A common mistake is to incorrectly compute the determinant or make an algebraic mistake when expanding and simplifying the equation. Careful attention to detail is required.
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