$ egin{vmatrix} -6 & -18 \ 4 & 20 \end{vmatrix} = (-6)(20) - (-18)(4) = -120 + 72 = -48 $

["Understanding 2x2 Determinants: A Step-by-Step Explanation of $$\n\begin{vmatrix} -6 & -18 \\ 4 & 20 \end{vmatrix} = -48", "Calculating a 2×2 determinant is a fundamental skill in linear algebra, useful in various mathematical and real-world applications—from solving systems of equations to understanding matrix properties. In this article, we’ll explain how to compute the determinant of the matrix\n$$\n\begin{vmatrix} -6 & -18 \ 4 & 20 \end{vmatrix}\n$$\nand verify the correct result: –48.", "---", "### What is a Determinant?", "The determinant of a 2×2 matrix\n$$\n\begin{pmatrix} a & b \ c & d \end{pmatrix}\n$$\nis computed using the formula:\n$$\n\ ext{determinant} = ad - bc\n$$\nThis value provides important information about the matrix, such as whether it is invertible and the area scaling factor of the linear transformation it represents.", "---", "### Step-by-Step Calculation", "Given the matrix:\n$$\n\begin{pmatrix} -6 & -18 \ 4 & 20 \end{pmatrix}\n$$", "Identify the elements:\n- ( a = -6 )\n- ( b = -18 )\n- ( c = 4 )\n- ( d = 20 )", "Apply the determinant formula:\n$$\n\ ext{determinant} = (-6)(20) - (-18)(4)\n$$", "Calculate each product:\n- ( (-6)(20) = -120 )\n- ( (-18)(4) = -72 ), so ( -(-72) = +72 )", "Now combine the results:\n$$\n-120 + 72 = -48\n$$", "Thus,\n$$\n\begin{vmatrix} -6 & -18 \ 4 & 20 \end{vmatrix} = -48\n$$", "---", "### Why Does This Formula Work?", "The determinant formula ( ad - bc ) sums the diagonal products and subtracts the off-diagonal product to capture how the matrix transforms area in the plane. A positive determinant indicates orientation preservation, while a negative one indicates a flip.", "---", "### Real-World Significance", "Determinants are widely used in:", "- Solving linear equations via Cramer’s Rule\n- Checking matrix invertibility\n- Calculating areas and volumes in geometry\n- Analyzing systems in engineering and physics", "Knowing how to compute determinants efficiently enhances your mathematical toolkit and problem-solving ability.", "---", "### Summary", "To evaluate:\n$$\n\begin{vmatrix} -6 & -18 \ 4 & 20 \end{vmatrix}\n$$\nuse the formula ( ad - bc ):\n=\n$$\n(-6)(20) - (-18)(4) = -120 + 72 = -48\n$$\nSo, the determinant is –48, confirming valuable insights about the matrix’s properties.", "---", "### SEO Keywords\n2x2 determinant calculation, how to compute determinant matrix, ad - bc formula 2×2 matrix, determinant of [[-6, -18], [4, 20]], linear algebra tutorial determinant, determinant example and explanation, Python matrix determinant code, matrix calculus formula", "---", "Mastering determinant calculations helps unlock more advanced math concepts—start from the basics, practice systematically, and build confidence in algebra and linear algebra!"]