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What is the determinant of the matrix\( \left[
\begin{array}{cc}
3 & -4 \\
7 & 2 \\
\end{array}
\right]\)
The determinant of a 2×2 matrix \(A=\left[
\begin{array}{cc}
a & b \\
c & d \\
\end{array}
\right]\) is written as det(A) = ad-bc.
Which of the following coefficient matrices represents the system of equations below?
8x-6y = 16
9x+4y = 61
You are helping your school organize a field trip to see a documentary at the local movie theater. The theater sells adult tickets (18+) for $11 and child tickets for $6. 5 adults and 32 children from the 11th grade will be attending, and 20 adults and 21 children will be attending in the 12th grade. Which of the following matrix products represents the total cost of tickets, in dollars, for both grades?
\(4 \left(
\begin{array}{cc}
-1 & 3 \\
4 & 1 \\
\end{array}
\right)+2 \left(
\begin{array}{cc}
2 & -2 \\
5 & 5 \\
\end{array}
\right)=?\)
If \(\left[
\begin{array}{cc}
7 & 4 \\
6 & -2 \\
\end{array}
\right]-3 \left[
\begin{array}{cc}
1 & -2 \\
2 & 5 \\
\end{array}
\right]=\)
Which of the following is equal to \(-3 \left[
\begin{array}{cc}
-3 & 0 \\
1 & 5 \\
\end{array}
\right]\)
If \(A=\left[
\begin{array}{cc}
4 & -1 \\
3 & 2 \\
\end{array}
\right]\) and \(B=\left[
\begin{array}{c}
3 \\
2 \\
\end{array}
\right]\), what is AB?