Question

Compute the determinant using elements in the first row:
A∣1 5 4∣
∣0 −7 −8∣
∣3 7 1∣

a. -7
b.32
c. -27
d. 3

Answer 1

Answer on Question #41341– Math - Linear Algebra

Question:

Compute the determinant using elements in the first row:

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

a. -7

b. 32

c. -27

d. 3

Solution:

$$A = \left| \begin{array}{ccc} 1 & 5 & 4 \\ 0 & -7 & -8 \\ 3 & 7 & 1 \end{array} \right| = (-1)^2 * 1 * \left| \begin{array}{cc} -7 & -8 \\ 7 & 1 \end{array} \right| + (-1)^3 * 5 * \left| \begin{array}{cc} 0 & -8 \\ 3 & 1 \end{array} \right| + (-1)^4 * 4 * \left| \begin{array}{cc} 0 & -7 \\ 7 & 1 \end{array} \right| = 1 * \left| \begin{array}{cc} -7 & -8 \\ 7 & 1 \end{array} \right| - 5 * \left| \begin{array}{cc} 0 & -8 \\ 3 & 1 \end{array} \right| + 4 * \left| \begin{array}{cc} 0 & -7 \\ 3 & 7 \end{array} \right| = (-7) + 56 - 5 * 24 + 4 * 21 = 13.$$

Answer:

The correct answer is 13.

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