Question

Compute the determinant using elements in the first row:
A∣∣∣∣1540−7−8371∣∣∣∣

Answer 1

Answer on Question # 41260 – Math – Linear Algebra

Compute the determinant using elements in the first row:

$$\left| \begin{array}{ccc} 1 & 5 & 4 \\ 0 & -7 & -8 \\ 3 & 7 & 1 \end{array} \right|$$

Solution.

$$\begin{array}{l} \left| \begin{array}{ccc} 1 & 5 & 4 \\ 0 & -7 & -8 \\ 3 & 7 & 1 \end{array} \right| = 1 \cdot \left| \begin{array}{cc} -7 & -8 \\ 7 & 1 \end{array} \right| - 5 \cdot \left| \begin{array}{cc} 0 & -8 \\ 3 & 1 \end{array} \right| + 4 \cdot \left| \begin{array}{cc} 0 & -7 \\ 3 & 7 \end{array} \right| = \\ = 1 \cdot ((-7) \cdot 1 - 7 \cdot (-8)) - 5 \cdot (0 \cdot 1 - 3 \cdot (-8)) + 4 \cdot (0 \cdot 7 - 3 \cdot (-7)) = \\ = 49 - 120 + 84 = 13. \end{array}$$

Answer.

13.

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