The order of a matrix is given by: Row × Column

(a)

$$ 3 \times 2 $$

(b)

$$ 1 \times 3 $$

(c)

$$ 3 \times 3 $$

(d)

$$ 2 \times 1$$

(e)

$$ 1 \times 1$$

(f)

$$ 2 \times 2$$

(a)

$$ \text{Equal} $$

(b)

$$ \text{Not equal, since the elements are different} $$

(c)

$$ \text{Not equal, since the order of the matrices are different} $$

(d)

$$ \text{Not equal, since the order of the matrices are different} $$

(i)

\begin{align*} \textbf{F} & = \left( \begin{matrix} 4 & 0 & 5 & 6 \\ 8 & 7 & 5 & 3 \end{matrix} \right) \end{align*}

(ii)

$$ \text{Banana} $$

(iii)

\begin{align*} \text{Sum of elements in first row} & = 4 + 0 + 5 + 6 \\ & = 15 \\ \\ \text{The boys in the class consume } & 15 \text{ fruits in total} \end{align*}

(iv) Find the sum of the elements in the last column of F

\begin{align*} \text{No. of students who like durian best} & = 6 + 3 \\ & = 9 \end{align*}

(a)

$$ \text{Not equal, since the order of the matrices are different} $$

(b)

$$ \text{Equal} $$

\begin{align} \textbf{B} & = \textbf{Q} \\ \\ \textbf{C} & = \textbf{O} \\ \\ \textbf{D} & = \textbf{I} \\ \\ \textbf{E} & = \textbf{H} \\ \\ \textbf{F} & = \textbf{P} \\ \\ \textbf{G} & = \textbf{L} \\ \\ \textbf{J} & = \textbf{N} \end{align}

(a)

\begin{align*} 2a & = 2 \\ a & = {2 \over 2} \\ a & = 1 \\ \\ b & = 3 \\ \\ c & = 5 \\ \\ k & = 7 \end{align*}

(b)

\begin{align*} a & = 3 \\ \\ b & = 13 \\ \\ d & = 7 \\ \\ c & = 6 \end{align*}

(c)

\begin{align*} 2x & = 14 \\ x & = {14 \over 2} \\ x & = 7 \\ \\ 2k & = 18 \\ k & = {18 \over 2} \\ k & = 9 \\ \\ 3y & = 15 \\ y & = {15 \over 3} \\ y & = 5 \\ \\ 6h & = 36 \\ h & = {36 \over 6} \\ h & = 6 \end{align*}

(d)

\begin{align*} 2x - 3 & = 7 \\ 2x & = 7 + 3 \\ 2x & = 10 \\ x & = {10 \over 2} \\ x & = 5 \\ \\ y + 4 & = 6 \\ y & = 6 - 4 \\ y & = 2 \end{align*}

(e)

\begin{align*} {1 \over 2}x & = 3 \\ x & = {3 \over {1 \over 2}} \\ x & = 6 \\ \\ h & = x + 4 \\ h & = 6 + 4 \\ h & = 10 \\ \\ k - 9 & = 5 \\ k & = 5 + 9 \\ k & = 14 \\ \\ 3y & = 27 \\ y & = {27 \over 3} \\ y & = 9 \end{align*}

(f)

\begin{align*} 2x - 5 & = 5 \\ 2x & = 5 \\ x & = {5 \over 2} \\ \\ y - 4 & = 0 \\ y & = 4 \\ \\ z + 3 & = 0 \\ z & = -3 \\ \\ 5k & = 0 \\ k & = {0 \over 5} \\ k & = 0 \end{align*}

(i)

\begin{align*} \textbf{S} & = \left( \begin{matrix} 0 & 3 & 1 & 7 \\ 3 & 0 & 4 & 2 \\ 1 & 4 & 0 & 5 \\ 7 & 2 & 5 & 0 \end{matrix} \right) \end{align*}

(ii)

$$ \text{5 goals} $$

(iii)

$$ \text{An impossible outcome in which a particular team plays against itself} $$

(iv)

\begin{align*} \text{Sum of elements in second row} & = 3 + 0 + 4 + 2 \\ & = 9 \\ \\ \text{Team } B \text{ scored } & 9 \text{ goals in total} \end{align*}

(v)

$$ \text{About the diagonal of zeros, the elements represents the goals scored in the same match} $$