What is the result of expanding the determinant of the matrix \begin{bmatrix} 4 & 6 \\ 2 & 4 \end{bmatrix}?
Understand the Problem
The question is asking for the determinant of a 2x2 matrix. We will calculate the determinant using the formula for a 2x2 matrix, which is ad - bc, where a, b, c, and d are the elements of the matrix.
Answer
The determinant of the matrix is $ad - bc$.
Answer for screen readers
The determinant of the matrix is given by the expression $ad - bc$.
Steps to Solve
- Identify the elements of the matrix
Let's denote the 2x2 matrix as:
$$ \begin{pmatrix} a & b \ c & d \end{pmatrix} $$
Here, $a$, $b$, $c$, and $d$ are the elements of the matrix.
- Substitute the elements into the determinant formula
The formula for the determinant of a 2x2 matrix is given by:
$$ \text{det}(A) = ad - bc $$
This is how we calculate the determinant.
- Calculate the determinant
Once we have the values of $a$, $b$, $c$, and $d$, we can substitute them into the determinant formula and calculate the result.
The determinant of the matrix is given by the expression $ad - bc$.
More Information
The determinant helps in understanding properties of a matrix, such as whether it is invertible. If the determinant is non-zero, it means the matrix has an inverse.
Tips
- Forgetting to multiply the elements in the correct order (i.e., ensuring you compute $ad$ and $bc$ correctly).
- Mixing up the signs when substituting values into the formula.
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