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Question 6 / 13 Your clients expect a $10 \%$ return on investment (ROI) for podcast ads and a $15 \%$ ROI for TV ads. How would you calculate the expected profit for a client who invests $\$ 5,500$ on a podcast ad and $\$ 10,000$ on a TV ad? $(\$ 5,500 \times 0.10)+(\$ 10,000 \times 0.15)$ $(\$ 5,500+\$ 10,000) \times 0.25$ $(\$ 5,500+\$ 10,000) / 0.25$ $(\$ 5,500 / 0.10)+(\$ 10,000 / 0.15)$ $(\$ 5,500+\$ 10,000) \times 25$

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Peter

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Solution By Steps

Step 1: Identify the given matrices

Given matrices are

A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} and

B = \begin{pmatrix} 5 & 6 \\ 7 & 8 \end{pmatrix}.

Step 2: Calculate the product of matrices A and B

To find

AB, we multiply each element of the rows of

A by the corresponding elements of the columns of

B and sum them up.

AB = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \begin{pmatrix} 5 & 6 \\ 7 & 8 \end{pmatrix} = \begin{pmatrix} (1 \cdot 5 + 2 \cdot 7) & (1 \cdot 6 + 2 \cdot 8) \\ (3 \cdot 5 + 4 \cdot 7) & (3 \cdot 6 + 4 \cdot 8) \end{pmatrix}

Step 3: Compute the elements of the product matrix

AB = \begin{pmatrix} (5 + 14) & (6 + 16) \\ (15 + 28) & (18 + 32) \end{pmatrix} = \begin{pmatrix} 19 & 22 \\ 43 & 50 \end{pmatrix}

Final Answer

The product of matrices

A and

B is

\boxed{\begin{pmatrix} 19 & 22 \\ 43 & 50 \end{pmatrix}}.

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