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For what real and positive value of x, if any, is the determinant of \(A=\left[
\begin{array}{cc}
6 & x \\
4 & x \\
\end{array}
\right]\) equal to 2x?
Here is an example of cross rates, as per Bloomberg, of some of the world’s largest economies on May 23, 2019:
\( \left[
\begin{array}{cccccc}
– & \text{USD} & \text{EUR} & \text{JPY} & \text{GBP} & \text{HKD} \\
\text{USD} & 1 & 1.1179 & 0.0091 & 1.2655 & 0.1274 \\
\text{EUR} & 0.8945 & 1 & 0.0082 & 1.132 & 0.114 \\
\text{JPY} & 109.57 & 122.51 & 1 & 138.672 & 13.9594 \\
\text{GBP} & 0.7901 & 0.8835 & 0.0072 & 1 & 0.1007 \\
\text{HKD} & 7.8492 & 8.7762 & 0.0716 & 9.9339 & 1 \\
\end{array}
\right] \)
(To see today’s cross rates, head over to Bloomberg)
How many Great British Pounds (GBP) are there in 1 Japanese Yen (JPY)?
What is the solution to the matrix product \(\left[
\begin{array}{cc}
\text{Sin} x & \text{Cos} x \\
\end{array}
\right] \left[
\begin{array}{c}
\text{Sin} x \\
\text{Cos} x \\
\end{array}
\right]\)
\(a_1\) and \( a_2\) in the 2×2 matrix below represent the prices per gallon of gasoline in Kansas City at Gas-Mart and Granno-Gas, respectively. Subscript[b, 1] and Subscript[b, 2] represent the prices per gallon of gasoline in Chicago at Gas-Mart and Granno-Gas, respectively. During a road trip from Kansas City to Chicago, you fill your tank with 15 gallons of gas at Gas-Plus in both cities. On your return trip, you decide to fill up your car 15 gallons at Granno-Gas in both cities. What does x-y represent if \(a_1+b_1<a_2+b_2\)?
\(\left[
\begin{array}{cc}
15 & 15 \\
\end{array}
\right] \left[
\begin{array}{cc}
a_1 & a_2 \\
b_1 & b_2 \\
\end{array}
\right]=\left[
\begin{array}{cc}
y & x \\
\end{array}
\right]\)