If H- 1 2 3- 2 3 1- 3 1 2 -G- 2 6 -10- 0 -4 8- 2 -8 4 -Find 3H-1-2G -3 Marks-

Given H=[ 1 amp;2 nbsp; amp;3; nbsp; 2 amp; 3 amp; 1; nbsp; 3 amp; 1 amp; 2 ]G=[ 2 amp; 6 amp; 10; nbsp; 0 amp; 4 amp; 8; nbsp; ...

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Standard X

Mathematics

Scalar Multiplication of a Matrix

If H=[ 1 2 3;...

Question

If $H = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 2 & 3 & 1 3 & 1 & 2 \end{matrix} ⎤ ⎥ ⎦ G = ⎡ ⎢ ⎣ \begin{matrix} 2 & 6 & - 10 0 & - 4 & 8 2 & - 8 & 4 \end{matrix} ⎤ ⎥ ⎦$

Find $3 H - \frac{1}{2} G$ [3 Marks]

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Solution

Given $H = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 2 & 3 & 1 3 & 1 & 2 \end{matrix} ⎤ ⎥ ⎦ G = ⎡ ⎢ ⎣ \begin{matrix} 2 & 6 & - 10 0 & - 4 & 8 2 & - 8 & 4 \end{matrix} ⎤ ⎥ ⎦$ [0.5 Mark]

$3 H = ⎡ ⎢ ⎣ \begin{matrix} 3 \times 1 & 3 \times 2 & 3 \times 3 3 \times 2 & 3 \times 3 & 3 \times 1 3 \times 3 & 3 \times 1 & 3 \times 2 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 3 & 6 & 9 6 & 9 & 3 9 & 3 & 6 \end{matrix} ⎤ ⎥ ⎦$ [0.5 Mark]

$\frac{1}{2} G = ⎡ ⎢ ⎣ \begin{matrix} 2 \div 2 & 6 \div 2 & - 10 \div 2 0 \div 2 & - 4 \div 2 & 8 \div 2 2 \div 2 & - 8 \div 2 & 4 \div 2 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 1 & 3 & - 5 0 & - 2 & 4 1 & - 4 & 2 \end{matrix} ⎤ ⎥ ⎦$ [1 Mark]

$3 H - \frac{1}{2} G = ⎡ ⎢ ⎣ \begin{matrix} 2 & 3 & 14 6 & 11 & - 1 8 & 7 & 4 \end{matrix} ⎤ ⎥ ⎦$ [1 Mark]

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If $H = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 2 & 3 & 1 3 & 1 & 2 \end{matrix} ⎤ ⎥ ⎦ G = ⎡ ⎢ ⎣ \begin{matrix} 2 & 6 & - 10 0 & - 4 & 8 2 & - 8 & 4 \end{matrix} ⎤ ⎥ ⎦$

Find $3 H - \frac{1}{2} G$

If
$H = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 2 & 3 & 1 3 & 1 & 2 \end{matrix} ⎤ ⎥ ⎦, G = ⎡ ⎢ ⎣ \begin{matrix} 2 & 6 & - 10 0 & - 4 & 8 2 & - 8 & 4 \end{matrix} ⎤ ⎥ ⎦$ ,
then find
$3 H - \frac{1}{2} G$ .

Q. (a)

If $H = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 2 & 3 & 1 3 & 1 & 2 \end{matrix} ⎤ ⎥ ⎦, G = ⎡ ⎢ ⎣ \begin{matrix} 2 & 6 & - 10 0 & - 4 & 8 2 & - 8 & 4 \end{matrix} ⎤ ⎥ ⎦$

Find $3 H - \frac{1}{2} G .$
$[3]$

(b) If $3 A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 2 2 & 1 & - 2 x & 2 & y \end{matrix} ⎤ ⎥ ⎦$ and $A \cdot A^{T} = I$ , then find the value of $x + y$ .
$[3]$

(c) If $A = [\begin{matrix} 2 & 5 1 & 3 \end{matrix}], B = [\begin{matrix} 4 & - 2 - 1 & 3 \end{matrix}]$ and $I$ is Identity matrix of same order and $A^{t}$ is the transpose of matrix $A$ find $A^{t} . B + B I$ .
$[4]$

Q. If

f^{2} (x) + 2 g^{2} (x) + 3 h^{2} (x) \leq 1

and

u (x) = 2 f (x) - 2 g (x) + 3 h (x),

then the maximum value of

u^{2} (x)

is equal to

Express askg using decimals.

(a) 2g (b) 100 g

(e) 26 kg50 g

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If $H = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 2 & 3 & 1 3 & 1 & 2 \end{matrix} ⎤ ⎥ ⎦ G = ⎡ ⎢ ⎣ \begin{matrix} 2 & 6 & - 10 0 & - 4 & 8 2 & - 8 & 4 \end{matrix} ⎤ ⎥ ⎦$

Find $3 H - \frac{1}{2} G$ [3 Marks]