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Chapter 11: Q. 52 (page 741)

In Problems 51–56, solve for x,
$|\begin{array}{l} x & 1 \\ 3 & x \end{array}| = - 2$

Short Answer

Expert verified

The value of xis $\pm 1$ .

Step by step solution

01

Step 1. Given Information

We are given,

$|\begin{array}{l} x & 1 \\ 3 & x \end{array}| = - 2$

We have to find the value of x.

02

Step 2. Solving the determinant

Solving the determinant, we get

$|\begin{array}{l} x & 1 \\ 3 & x \end{array}| = - 2 x (x) - 1 (3) = - 2 x^{2} - 3 = - 2 x^{2} = 1 x = \pm 1$

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Most popular questions from this chapter

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

x + y - z = 6

3x - 2y + z = -5

x + 3y - 2z = 14

The perimeter of a rectangle is $16$ inches, and its area is $15 i n c h e s^{2}$ . What are its dimensions?

In Problems 35–42, graph each system of inequalities by hand.

$\{\begin{cases} x^{2} + y^{2} \geq 9 \\ x + y \leq 3 \end{cases}$

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

$y = 3 x - 5; x^{2} + y^{2} = 5$

In Problems 23–34, graph each system of linear inequalities by hand. Verify your results using a graphing utility

$\{\begin{cases} 2 x + y \geq 0 \\ 2 x + y \geq 2 \end{cases}$

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