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Chapter 11: Q. 18 (page 795)

find the value of each determinant.
$|\begin{matrix} 2 & - 4 & 6 \\ 1 & 4 & 0 \\ - 1 & 2 & - 4 \end{matrix}|$

Short Answer

Expert verified

The determinant of the given matrix is $- 4$ .

Step by step solution

Step 1. Given

$|\begin{matrix} 2 & - 4 & 6 \\ 1 & 4 & 0 \\ - 1 & 2 & - 4 \end{matrix}|$

Step 2. Calculation

$|\begin{matrix} 2 & - 4 & 6 \\ 1 & 4 & 0 \\ - 1 & 2 & - 4 \end{matrix}| = 2 [(4 \times - 4) - (0 \times 2)] - (- 4) [(- 4) \times 1 - 0 \times (- 1)] + 6 [2 \times 1 - 4 \times (- 1)] = - 4$

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Most popular questions from this chapter

In Problems, use the division algorithm to rewrite each improper fraction as the sum of a quotient and proper fraction. Find the partial fraction decomposition of the proper fraction. Finally, express the improper fraction as the sum of a quotient and the partial fraction decomposition.

$\frac{x^{4} - 5 x^{2} + x - 4}{x^{2} + 4 x + 4}$

Solve each system of equations. If the system has no solution, say that it is inconsistent.

$\{\begin{matrix} x + 2 y = 4 \\ 2 x + 4 y = 8 \end{matrix}$

Verify that the values of the variables listed are solutions of the system of equations.

$\{\begin{matrix} 3 x + 2 y = 2 \\ x - 7 y = - 30 \end{matrix} x = - 2, y = 4; (- 2, 4)$

In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.

$x y = 4; x^{2} + y^{2} = 8$

The ratio of a to b is $4 : 3$ . The sum of a and b is $14$ . What is the ratio of $a - b$ to $a + b$ ?

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find the value of each determinant.2-46140-12-4

Short Answer

Step by step solution

Step 1. Given

Step 2. Calculation

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Most popular questions from this chapter

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find the value of each determinant.
$|\begin{matrix} 2 & - 4 & 6 \\ 1 & 4 & 0 \\ - 1 & 2 & - 4 \end{matrix}|$