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=AxB=\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.