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Chapter 8: Problem 9

Find the determinant of the matrix. $$\left[\begin{array}{rr} -7 & 6 \\ \frac{1}{2} & 3 \end{array}\right]$$

Short Answer

Expert verified
The determinant of the matrix is -24.

Step by step solution

01

Identify Matrix Elements

Firstly, identify the elements of the matrix \(\left[\begin{array}{rr}-7 & 6 \ rac{1}{2} & 3\end{array}\right]\). They correspond to \[a = -7\], \[b = 6\], \[c = \frac{1}{2}\] and \[d = 3\].
02

Apply the Formula

Then use the determinant formula for 2x2 matrix, which is \[|A| = a*d - b*c\]. Substituting given values: \[|A| = -7*3 - 6*\frac{1}{2}\].
03

Calculate Result

Do the multiplications and subtraction: |-21 - 3|= -24.

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Most popular questions from this chapter

Find the domain of the function and identify any horizontal or vertical asymptotes. $$f(x)=\frac{x-4}{x^{2}+16}$$

Solve for \(x\) $$\left|\begin{array}{cc} 2 x & 1 \\ -1 & x-1 \end{array}\right|=x$$

Find the general form of the equation of the line that passes through the two points. \((-4,12),(4,2)\)

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The sums have been evaluated. Solve the given system for \(a\) and \(b\) to find the least squares regression line for the points. Use a graphing utility to confirm the results. $$\left\\{\begin{array}{l} 5 b+10 a=20.2 \\ 10 b+30 a=50.1 \end{array}\right.$$
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