Questions: Запишите разложение определителя по 2 -й строке 1 -5 -3 a b c -2 2 5 =□ a+□ b+□ c Проверить

Solution Steps

To find the determinant of the original 3x3 matrix using cofactor expansion along the second row, we first need to calculate the determinants of the following 2x2 matrices:

1. For \( a \): \[ \left|\begin{matrix}-5 & -3\\2 & 5\end{matrix}\right| = (-1)^0 \times (-5) \times \frac{19}{5} = -19.00 \]

2. For \( b \): \[ \left|\begin{matrix}1 & -3\\-2 & 5\end{matrix}\right| = (-1)^1 \times (-2) \times \left(-\frac{1}{2}\right) = -1.00 \]

3. For \( c \): \[ \left|\begin{matrix}1 & -5\\-2 & 2\end{matrix}\right| = (-1)^1 \times (-2) \times (-4) = -8.00 \]

Using the determinants calculated above, we can express the determinant of the original matrix as follows: \[ \left|\begin{array}{ccc} 1 & -5 & -3 \\ a & b & c \\ -2 & 2 & 5 \end{array}\right| = -19.00 \cdot a - (-1.00) \cdot b - 8.00 \cdot c \] This simplifies to: \[ \left|\begin{array}{ccc} 1 & -5 & -3 \\ a & b & c \\ -2 & 2 & 5 \end{array}\right| = -19.00 a + 1.00 b - 8.00 c \]

Final Answer