<p>Four shops sell different brands of running shoes: Mizuho, Azizs, New Ballast and Nikuu. The table below shows the number of shoes sold by the four shops in a particular week.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 500px;"><colgroup><col style="width: 100px;"><col style="width: 100px;"><col style="width: 100px;"><col style="width: 100px;"><col style="width: 100px;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center">Shop/Brand</th><th style="text-align: center; --cell-justify: center">Mizuho</th><th style="text-align: center; --cell-justify: center">Azizs</th><th style="text-align: center; --cell-justify: center">New Ballast</th><th style="text-align: center; --cell-justify: center">Nikuu</th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">Running Sports</td><td style="text-align: center; --cell-justify: center">$10$</td><td style="text-align: center; --cell-justify: center">$12$</td><td style="text-align: center; --cell-justify: center">$15$</td><td style="text-align: center; --cell-justify: center">$8$</td></tr><tr><td style="text-align: center; --cell-justify: center">Real Runners</td><td style="text-align: center; --cell-justify: center">$5$</td><td style="text-align: center; --cell-justify: center">$11$</td><td style="text-align: center; --cell-justify: center">$8$</td><td style="text-align: center; --cell-justify: center">$17$</td></tr><tr><td style="text-align: center; --cell-justify: center">Run Fast</td><td style="text-align: center; --cell-justify: center">$16$</td><td style="text-align: center; --cell-justify: center">$4$</td><td style="text-align: center; --cell-justify: center">$7$</td><td style="text-align: center; --cell-justify: center">$6$</td></tr><tr><td style="text-align: center; --cell-justify: center">Strong Runners</td><td style="text-align: center; --cell-justify: center">$6$</td><td style="text-align: center; --cell-justify: center">$8$</td><td style="text-align: center; --cell-justify: center">$4$</td><td style="text-align: center; --cell-justify: center">$11$</td></tr></tbody></table></div></div>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Represent the information given in the table above by a $4 \times 4$ matrix $S$.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Mizuho shoes are sold at $\$160$ each, Azizs shoes at $\$120$ each, New Ballast shoes at $\$120$ each and Nikuu shoes at $\$140$ each. Write down a $4 \times 1$ matrix $P$ to represent the selling prices, in dollars, of the different brands of shoes.</span></div></li><li><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find $SP$.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Explain what the elements in the matrix $SP$ represent.</span></div></li><li><div class="list-item-content"><span class="list-item-text">It is given that&nbsp;$T = \begin{pmatrix} 1 \\ 1 \\ 1 \\ 1 \end{pmatrix}$. Evaluate $ST$ and explain what the elements of $ST$ represent.</span></div></li></ol></li></ol>

Four shops sell different brands of running shoes: Mizuho, Azizs, New Ballast and Nikuu. The table below shows the number of shoes sold by the four shops in a particular week.

Represent the information given in the table above by a $4 \times 4$ matrix $S$.

Mizuho shoes are sold at $\$160$ each, Azizs shoes at $\$120$ each, New Ballast shoes at $\$120$ each and Nikuu shoes at $\$140$ each. Write down a $4 \times 1$ matrix $P$ to represent the selling prices, in dollars, of the different brands of shoes.

Explain what the elements in the matrix $SP$ represent.

It is given that $T = \begin{pmatrix} 1 \\ 1 \\ 1 \\ 1 \end{pmatrix}$. Evaluate $ST$ and explain what the elements of $ST$ represent.

Matrices - Application of Matrices

Question bf03f389