[1 Mark Question Answer]

Question 11 Mark

Given $\left[\begin{array}{cc}2 & 1 \\ -3 & 4\end{array}\right], X=\left[\begin{array}{l}7 \\ 6\end{array}\right]$ the order of the matrix $X$

Answer

We have
$\left[\begin{array}{cc} 2 & 1 \\-3 & 4\end{array}\right], X =\left[\begin{array}{l}7 \\6\end{array}\right]$
We see that $2 \times 2 \times 2 \times 1=2 \times 1$
$\Rightarrow$ The order of $X$ is $2 \times 1$.

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Question 21 Mark

If $\left[\begin{array}{ll}1 & 3 \\ 0 & 0\end{array}\right]\left[\begin{array}{c}2 \\ -1\end{array}\right]=\left[\begin{array}{l}x \\ 0\end{array}\right]$ Find the value of $x$

Answer

$\begin{aligned} & {\left[\begin{array}{ll}1 & 3 \\ 0 & 0\end{array}\right]\left[\begin{array}{c}2 \\ -1\end{array}\right]=\left[\begin{array}{l}x \\ 0\end{array}\right]} \end{aligned} $
$ \Rightarrow\left[\begin{array}{cc}2 & -3 \\ 0 & 0\end{array}\right]=\left[\begin{array}{l}x \\ 0\end{array}\right] $
$ \Rightarrow\left[\begin{array}{c}-1 \\ 0\end{array}\right]=\left[\begin{array}{l}x \\ 0\end{array}\right]$
Comparing the corresponding elements $x=-1$

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Question 31 Mark

Construct a $2 \times 2$ matrix whose elements $a_{ij}$ are given by $a_{ij} = i.j$

Answer

It can be $\left[\begin{array}{ll}1 & 2 \\ 2 & 4\end{array}\right]$.

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Question 41 Mark

Construct a $2 \times 2$ matrix whose elements $a_{ij}$ are given by $a_{ij} = 2i – j$

Answer

It can be $\left[\begin{array}{ll}1 & 0 \\ 3 & 2\end{array}\right]$

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Question 51 Mark