Chapter C, Problem C.6E

To determine

The ANSWER of the equation using MATLAB.

Answer to Problem C.6E

$y=0.5-10=-9.5$.

Explanation of Solution

Given:

$y=0.5-w,where$$x=\left[\begin{array}{cc}2& \begin{array}{ccc}\begin{array}{cc}64& 82\end{array}& 106& 94\end{array}\end{array}\right]$.

$x=\left[\begin{array}{cc}2& \begin{array}{ccc}\begin{array}{cc}64& 82\end{array}& 106& 94\end{array}\end{array}\right]$ and $w=\left[\begin{array}{cc}\begin{array}{cc}\begin{array}{cc}\begin{array}{cc}5& 6\end{array}& 7\end{array}& 8\end{array}& 9\end{array}\right]$.

Calculation:

Using matrices we can determine value of $y=0.5-w$, before we must understand matrices.

It most popular applications for engineering curricula it like a vector, here we demonstrate some example how to use MATLAB for solving matrices. A vector is important type of a matrix which has single row or column. An instance of matrix is:

$A=\left[\begin{array}{ccc}9& 5& 7\\ 8& 6& 4\\ 4& 2& 1\end{array}\right]$.

Every matrix has certain size depending on its number element exist in the column and rows, such as in above example size of $A=3\times 3$ means three rows and three columns. The command which give size of matrix is size, for example it can be written in MATLAB command format “size(A)” then it would return “3 3” for above matrix.

We can find a position of each element in matrix as first column and first row means we could written as $a_{11}$ and the value would be 9.

Suppose we require to take element such $a_{1.1},a_{1.2},a_{2.1},and{a}_{22}$, and many more then we should enter as $“A\left(1:2,1:2\right).”$.

now come to given problem, $x=\left[2648210694\right]andw=\left[56789\right].$.

By using MATLAB, multiply matrices of same size $x=1\times 1$ and $w=1\times 1$.

Multiplying first row of first matrices and second matrices of first row then it results 10.

So $y=0.5-10=-9.5$.

Some common method for multiplying two matrices shown below.

$A=\left[\begin{array}{cc}{a}_{1,1}& a_{1,2}\\ a_{2,1}& a_{2,2}\end{array}\right]$$B=\left[\begin{array}{cc}{b}_{1,1}& b_{1,2}\\ b_{2,1}& b_{2,2}\end{array}\right]$.

$A*B$ Becomes.

$\left[\begin{array}{cc}{a}_{1,1}& a_{1,2}\\ a_{2,1}& a_{2,2}\end{array}\right]$ $\times$ $\left[\begin{array}{cc}{b}_{1,1}& b_{1,2}\\ b_{2,1}& b_{2,2}\end{array}\right]$= $$ $\left[\begin{array}{cc}(a_{1,1}\times b_{1,1}+a_{1,2}\times b_{{}_{2,1}})& (a_{1,1}\times b_{1,2}+a_{1,2}\times b_{{}_{2,2}})\\ (a_{2,1\times }{b}_{1,1}+a_{2,2}\times b_{2,1})& (a_{2,1\times }{b}_{1,2}+a_{2,2}\times b_{2,2})\end{array}\right]$.

Conclusion:

MATLAB follows the matrices rules so we must write in matrix form.