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Problem 1

Refer to the following matrices: $A=\left[\begin{array}{rrrr}2 & -3 & 9 & -4 \\ -11 & 2 & 6 & 7 \\ 6 & 0 & 2 & 9 \\ 5 & 1 & 5 & -8\end{array}\right]$ $B=\left[\begin{array}{rrr}3 & -1 & 2 \\ 0 & 1 & 4 \\ 3 & 2 & 1 \\ -1 & 0 & 8\end{array}\right]$ \(C=\left[\begin{array}{lllll}1 & 0 & 3 & 4 & 5\end{array}\right]\) \(D=\left[\begin{array}{r}1 \\ 3 \\ -2 \\ 0\end{array}\right]\) What is the size of \(A ?\) Of \(B ?\) Of \(C\) ? Of \(D ?\)

Expert verified

The sizes of the given matrices are: \(A: 4\times4\), \(B: 4\times3\), \(C: 1\times5\), and \(D: 4\times1\).

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Chapter 5

Compute the indicated products. $\left[\begin{array}{rrr}6 & -3 & 0 \\ -2 & 1 & -8 \\ 4 & -4 & 9\end{array}\right]\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]$

Chapter 5

Compute the indicated products. $\left[\begin{array}{rr}2 & 4 \\ -1 & -5 \\ 3 & -1\end{array}\right]\left[\begin{array}{rrr}2 & -2 & 4 \\ 1 & 3 & -1\end{array}\right]$

Chapter 5

Write the given system of linear equations in matrix form. $\begin{aligned} 2 x-3 y+4 z &=6 \\ 2 y-3 z &=7 \\ x-y+2 z &=4 \end{aligned}$

Chapter 5

Kaitlin and her friend Emma returned to the United States from a tour of four cities: Oslo, Stockholm, Copenhagen, and Saint Petersburg. They now wish to exchange the various foreign currencies that they have accumulated for U.S. dollars. Kaitlin has 82 Norwegian krones, 68 Swedish krones, 62 Danish krones, and 1200 Russian rubles. Emma has 64 Norwegian krones, 74 Swedish krones, 44 Danish krones, and 1600 Russian rubles. Suppose the exchange rates are U.S. \(\$ 0.1651\) for one Norwegian krone, U.S. \(\$ 0.1462\) for one Swedish krone, U.S. \(\$ 0.1811\) for one Danish krone, and U.S. \(\$ 0.0387\) for one Russian ruble. a. Write a \(2 \times 4\) matrix \(A\) giving the values of the various foreign currencies held by Kaitlin and Emma. (Note: The answer is not unique.) b. Write a column matrix \(B\) giving the exchange rate for the various currencies. c. If both Kaitlin and Emma exchange all their foreign currencies for U.S. dollars, how many dollars will each have?

Chapter 5

The sizes of matrices \(A\) and \(B\) are given. Find the size of \(A B\) and \(B A\) whenever they are defined. \(A\) is of size \(2 \times 3\), and \(B\) is of size \(3 \times 5\).

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