The image shows a matrix. Since no specific operation is requested, I will find the determinant of the given matrix, which is a common first step when dealing with matrices containing variables. The given matrix is: O = 2 & 2p 1 & 3 Step 1: Recall the formula for the determinant of a 2 × 2 matrix. For a matrix a & b c & d , the determinant is ad − bc. Step 2: Substitute the values from the given matrix into the formula. Here, a=2, b=2p, c=1, and d=3. det(O) = (2)(3) − (2p)(1) Step 3: Perform the multiplication and subtraction. det(O) = 6 − 2p The determinant of the matrix is 6 − 2p.

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June 16, 2026Mathematics

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6 - 2p

Step-by-step solution

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The image shows a matrix. Since no specific operation is requested, I will find the determinant of the given matrix, which is a common first step when dealing with matrices containing variables.

The given matrix is:

O = \begin{pmatrix} 2 & 2p \\ 1 & 3 \end{pmatrix}

Recall the formula for the determinant of a $2 \times 2$ matrix.
For a matrix $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$ , the determinant is $ad - bc$ .
Substitute the values from the given matrix into the formula.
Here, $a=2$ , $b=2p$ , $c=1$ , and $d=3$ .
$\det(O) = (2)(3) - (2p)(1)$
Perform the multiplication and subtraction.
$\det(O) = 6 - 2p$
The determinant of the matrix is $6 - 2p$ .

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