Answer to Matrix Addition Quiz

To find the value of the ${ij}$th element of Matrix $D$ , we need to calculate:

$D=A+B-C$

$D=\begin{bmatrix} 3 &0.6 &4&-3\\ -1.3 &4 &0&8.6\\7&0 &-8& 0.006\end {bmatrix}+\begin{bmatrix} 3 &-5.76 &45&0\\ 2 &-2 &1.3&9\\-9&0 &0& 0\end{bmatrix}-\begin{bmatrix} 0 &1009 &-66.7849&90\\ 0 &5 &4&-0.07\\-7.7&0 &0& 0\end{bmatrix}$

We can calculate all $12$ elements of matrix $D$, but it will be even easier to simply find only at the relevant elements.

let's find only the necessary elements of matrix $D$:

$D_{23}$ and and $D_{31}$

$D_{23}=0+1.3-4=-2.7$

$D_{31}=7-9-(-7.7)=5.7$

Answer to Scalar Multiplication of Matrix Quiz

To find the value of the ${ij}$th element of Matrix $D$ , we need to calculate:

$D=0.2A+(-5)B-2C$

$D=0.2\begin{bmatrix} 3 &0.6 &4&-3\\ -1.3 &4 &0&8.6\\7&0 &-8& 0.006\end{bmatrix}-5\begin{bmatrix} 3 &-5.76 &45&0\\ 2 &-2 &1.3&9\\-9&0 &0& 1\end{bmatrix}-2\begin{bmatrix} 0 &1009 &-66.7849&90\\ 0 &5 &4&-0.07\\0&0 &0& 0\end{bmatrix}$

Again, we can calculate all $12$ elements of matrix $D$, but it will be even easier to simply find only at the relevant elements.

let's find only the necessary elements of matrix $D$:

$D_{11}$ and and $D_{24}$

$D_{11}=0.2 \cdot 3-5\cdot 3-2\cdot 0=-14.4$

$D_{24}=0.2 \cdot 8.6-5\cdot 9-2\cdot (-0.07)=-43.14$

Answer to Square Matrix Multiplication Quiz

$A=\begin{bmatrix} 3 &1 &2\\ -5 &4 &1\\0&3&-8\end{bmatrix}$

$B=\begin{bmatrix} 0 &5&-1\\ 3 &2 &-1\\10&0.5&4\end{bmatrix}$

If
$C=A$ x $B=\begin{bmatrix} 3 &1 &2\\ -5 &4 &1\\0&3&-8\end{bmatrix}$x$\begin{bmatrix} 0 &5&-1\\ 3 &2 &-1\\10&0.5&4\end{bmatrix}=\begin{bmatrix} 23 & 18 &4\\ 22 &-16.5 &5\\-71&2&-35\end{bmatrix}$

Then $c_{23}=5$

If
$C=B$ x $A=$$\begin{bmatrix} 0 &5&-1\\ 3 &2 &-1\\10&0.5&4\end{bmatrix}$x $\begin{bmatrix} 3 &1 &2\\ -5 &4 &1\\0&3&-8\end{bmatrix}=\begin{bmatrix} -25 & 17 &13\\ -1 &8 &16\\27.5&24&-11.5\end{bmatrix}$

Then $c_{23}=16$

Notice that matrix multiplication is not commutative.
$B$ x $A\not =A$ x $B$.

Answer to Matrix Multiplication Quiz

If: $A=\begin{bmatrix} 0.6 &-15 &2&5&98\end{bmatrix}$

$B=\begin{bmatrix} 2&2&-4\\ 9 &-14 &0\\13&-0.5&44\\1&9&4\\0&0&5\end{bmatrix}$

$C=A$x$B$=$\begin{bmatrix} 0.6 &-15 &2&5&98\end{bmatrix}$x$\begin{bmatrix} 2&2&-4\\ 9 &-14 &0\\13&-0.5&44\\1&9&4\\0&0&5\end{bmatrix}= \begin{bmatrix} -102.8 &255.2 &595.6\end{bmatrix}$

The result is a row vector with 3 elements. Hence the number of rows is $1$ and the number of columns is $3$.

The value of $c_{13}$ is 595.6.

There is no valid answer to section (d) as the dimensions of $B$ and $A$ do not match.