EXERCISE The numbers of calories burned by individuals of...

EXERCISE The numbers of calories burned by individuals of different body weights performing different types of aerobic exercises for a 20-minute time period are shown in matrix $A$. \begin{equation} \stackrel{\mbox{Calories burned}}{ \overbrace{ \begin{array}{@{}r@{\quad}ccrr@{}} \textrm{120-lb} & \textrm{150-lb} \\ \textrm{person} & \textrm{person} \end{array}}} \end{equation} \begin{equation} \left. P=\left[\begin{array}{@{}r@{\quad}ccrr@{}} 109 & 136 \\ 127 & 159 \\ 64 & 79 \end{array}\right] \begin{array}{r} \textrm{Bicycling} \\ \textrm{Jogging} \\ \textrm{Walking} \end{array}\right\} \end{equation} (a) A 120-pound person and a 150-pound person bicycled for 40 minutes, jogged for 10 minutes, and walked for 60 minutes. Organize the time they spent exercising in a matrix $B$. (b) Compute $BA$ and interpret the result.

EXERCISE The numbers of calories burned by individuals of different body weights performing different types of aerobic exercises for a 20-minute time period are shown in matrix $A$.

\begin{equation}
\stackrel{\mbox{Calories burned}}{
\overbrace{
\begin{array}{@{}r@{\quad}ccrr@{}}
\textrm{120-lb} & \textrm{150-lb} \\
\textrm{person} & \textrm{person}
\end{array}}}
\end{equation}

\begin{equation}
\left.
P=\left[\begin{array}{@{}r@{\quad}ccrr@{}}
109 & 136 \\
127 & 159 \\
64 & 79
\end{array}\right] \begin{array}{r} \textrm{Bicycling} \\ \textrm{Jogging} \\ \textrm{Walking} \end{array}\right\}
\end{equation}

(a) A 120-pound person and a 150-pound person bicycled for 40 minutes, jogged for 10 minutes, and walked for 60 minutes. Organize the time they spent exercising in a matrix $B$.
(b) Compute $BA$ and interpret the result.

Transcript

00:01 In this question, it is being said that a 120 pound person and a 150 pound person has bicycle for 40 minutes.

00:09 It's noted down as i'm saying.

00:12 A bicycle for 40 minutes.

00:18 Then apart from that, job for 10 minutes, right? job for 10 minutes.

00:29 And the walk for 60 minutes.

00:32 So, walked for 60 minutes.

00:34 60 minutes fine now what is being asked in the question is you just have to organize this time in matrix b so for that the matrix b is going to be a row matrix what does that mean it is just going to have one row and three columns right so for that what i'm going to do is you can just write that as 40 10 and 60 but in the question it was already stated that it is a 20 or time period matrix right so for that i'm just going to decide between every element of the matrix b by 20 so what you'll get 40 divided by 20 is 2 10 divided by 20 is 0 .5 and 60 divided by 20 is 3 so this is the required matrix b right coming on to part b now what is being asked over here you just have to compute b a so matrix b we just found out note down the elements 2 .4.

01:34 And 3 and what was matrix ab i mean a c b a c b a just have to find out the product of the two matrices so note down the elements of matrix a as well one zero nine one hundred and thirty six one hundred and twenty seven one hundred and fifty nine sixty four and seventeen nine so the first matrix b is of the order one by three the third second one matrix a is of the order three by two that means the matrix b is going to be of the order 1 by 2, row matrix having 2 columns.

02:12 So how you are going to find that? simply just multiply the elements of the row of matrix b with the columns of matrix a.

02:19 So 2 times 109 plus 0 .5 multiplied by 127 plus 3 times 64.

02:27 So that will give you 473 .5...

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