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Chapter 11: Q. 9 (page 740)

Find the value of the determinant.
$|\begin{matrix} - 3 & - 1 \\ 4 & 2 \end{matrix}|$

Short Answer

Expert verified

$|\begin{matrix} - 3 & - 1 \\ 4 & 2 \end{matrix}| = - 2$

Step by step solution

Step 1. Given information

We have been given:

$|\begin{matrix} - 3 & - 1 \\ 4 & 2 \end{matrix}|$

We have to find the value of this determinant.

Step 2. Use formula D=abcd=a⋅d-c⋅b.

$|\begin{matrix} - 3 & - 1 \\ 4 & 2 \end{matrix}| = - 3 \times 2 - 4 \times (- 1) = - 6 + 4 = - 2$

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Most popular questions from this chapter

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

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

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

$\{\begin{array}{r} \begin{array}{rcl} 4 x - z & = & 7 \\ 8 x + 5 y - z & = & 0 \end{array} \\ - x - y + 5 z = 6 \end{array} x = 2, y = - 3, z = 1; (2, - 3, 1)$

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.

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

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

$x^{2} + y^{2} = 10; y = x + 2$

$\frac{x^{5} + x^{4} - x^{2} + 2}{x^{4} - 2 x^{2} + 1}$

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Find the value of the determinant.-3-142

Short Answer

Step by step solution

Step 1. Given information

Step 2. Use formula D=abcd=a⋅d-c⋅b.

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Most popular questions from this chapter

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Find the value of the determinant.
$|\begin{matrix} - 3 & - 1 \\ 4 & 2 \end{matrix}|$