[3 marks sum]

Question 13 Marks

Evaluate: $\left[\begin{array}{cc}4 \sin 30^{\circ} & 2 \cos 60^{\circ} \\ \sin 90^{\circ} & 2 \cos 0^{\circ}\end{array}\right]\left[\begin{array}{ll}4 & 5 \\ 5 & 4\end{array}\right]$.

Answer

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Question 23 Marks

If $A =\left[\begin{array}{cc}3 & -2 \\ -1 & 4\end{array}\right], B =\left[\begin{array}{l}6 \\ 1\end{array}\right], C =\left[\begin{array}{r}-4 \\ 5\end{array}\right]$ and $D =\left[\begin{array}{l}2 \\ 2\end{array}\right]$, find $AB +2 C -4 D$.

Answer

Self

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Question 33 Marks

Find $x$ and $y$ if $\left[\begin{array}{cc}2 x & x \\ y & 3 y\end{array}\right]\left[\begin{array}{l}3 \\ 2\end{array}\right]=\left[\begin{array}{l}16 \\ 9\end{array}\right]$.

Answer

Self

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Question 43 Marks

If $A =\left[\begin{array}{cc}p & 0 \\ 0 & 2\end{array}\right], B =\left[\begin{array}{cc}0 & -q \\ 1 & 0\end{array}\right]$ and $C =\left[\begin{array}{cc}2 & -2 \\ 2 & 2\end{array}\right]$ and $BC = C ^2$, find the values of $p$ and $q$.

Answer

Self

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Question 53 Marks

If $\left[\begin{array}{cc}1 & 4 \\ -2 & 3\end{array}\right]+2 M=3\left[\begin{array}{cc}3 & 2 \\ 0 & -3\end{array}\right]$, find the matrix $M$.

Answer

Self

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Question 63 Marks

Given $A =\left[\begin{array}{ll}x & 3 \\ y & 3\end{array}\right]$
If $A ^2=3 I$, where $I$ is the identity matrix of order 2 , find $x$ and $y$.

Answer

Self

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Question 73 Marks

Simplify : $\sin A\left[\begin{array}{cc}\sin A- & \cos A \\ \cos A & \sin A\end{array}\right]+\cos A\left[\begin{array}{cc}\cos A & \sin A \\ -\sin A & \cos A\end{array}\right]$

Answer

Self

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Question 83 Marks

Find the value of ' $x$ ' and ' $y$ ' if : $
2\left[\begin{array}{cc}
x & 7 \\
9 & y-5
\end{array}\right]+\left[\begin{array}{cc}
6 & -7 \\
4 & 5
\end{array}\right]=\left[\begin{array}{cc}
10 & 7 \\
22 & 15
\end{array}\right]
$

Answer

Self

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Question 93 Marks

Given matrix $A =\left[\begin{array}{cc}4 \sin 30^{\circ} & \cos 0^{\circ} \\ \cos 0^{\circ} & 4 \sin 30^{\circ}\end{array}\right]$ and $B =\left[\begin{array}{l}4 \\ 5\end{array}\right]$ If $AX = B$
$(a)$ Write the order of matrix $X .$
$(b)$ Find the matrix $X .$

Answer

Self

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Question 103 Marks

If $A =\left[\begin{array}{cc}3 & -1 \\ 0 & 2\end{array}\right]$, find matrix B such that $A ^2-2 B=3 A+5 I$, where $I$ is a $2 \times 2$ identity matrix.

Answer

Self

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Mathematics [3 marks sum]

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