Find the determinant

April 9, 2026Mathematics

ScanSolve AI Answer

April 9, 2026

Answer

Step 1: Identify the elements of the matrix. The given matrix is a $2 \times 2$ matrix: $A = \begin{bmatrix} -3 & -3 \\ 4 & 1 \end{bmatrix}$

Step 2: Calculate the determinant of the $2 \times 2$ matrix. The formula for the determinant of a $2 \times 2$ matrix $\begin{bmatrix} a & b \\ c & d \end{bmatrix}$ is $ad - bc$ . Applying this formula to matrix $A$ : $\det(A) = (-3)(1) - (-3)(4)$

Step 3: Perform the multiplication. $\det(A) = -3 - (-12)$

Step 4: Simplify the expression. $\det(A) = -3 + 12$ $\det(A) = 9$

The determinant of the matrix is $\boxed{9}$ .

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Identify the elements of the matrix. The given matrix is a 2 × 2 matrix: A = -3 & -3 \\ 4 & 1 Step 2: Calculate the determinant of the 2 × 2 matrix.

Asked on April 9, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 9, 2026

Step 1: Identify the elements of the matrix. The given matrix is a 2 × 2 matrix: A = -3 & -3 \\ 4 & 1 Step 2: Calculate the determinant of the 2 × 2 matrix. The formula for the determinant of a 2 × 2 matrix a & b \\ c & d is ad - bc. Applying this formula to matrix A: (A) = (-3)(1) - (-3)(4) Step 3: Perform the multiplication. (A) = -3 - (-12) Step 4: Simplify the expression. (A) = -3 + 12 (A) = 9 The determinant of the matrix is 9.