Wherever possible- write each of the following as a single matrix i - 1 2- 3 4 - - -1 -2- 1 -7 - ii - 2 3 4- 4 6 7 - - 0 2 3- 6 -1 0 - iii - 0 1 2- 4 6 7 - - 3 4- 6 8 -

(i)[ 1 amp;2; 3 amp;4 ]+ [ 1 amp; 2; 1 amp; 7 ] = [ 1 1 amp;2 2; 3+1 amp;4 7 ]= [ 0 amp;0; 4 amp; 3 ] (ii)[ 2 amp ...

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Byju's Answer

Standard X

Mathematics

Addition and Subtraction of a Matrix

Wherever poss...

Question

Wherever possible, write each of the following as a single matrix

$(i) [\begin{matrix} 1 & 2 3 & 4 \end{matrix}] + [\begin{matrix} - 1 & - 2 1 & - 7 \end{matrix}]$
$(i i) [\begin{matrix} 2 & 3 & 4 4 & 6 & 7 \end{matrix}] - [\begin{matrix} 0 & 2 & 3 6 & - 1 & 0 \end{matrix}]$
$(i i i) [\begin{matrix} 0 & 1 & 2 4 & 6 & 7 \end{matrix}] + [\begin{matrix} 3 & 4 6 & 8 \end{matrix}]$

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Solution

(i) $[\begin{matrix} 1 & 2 3 & 4 \end{matrix}] + [\begin{matrix} - 1 & - 2 1 & - 7 \end{matrix}] = [\begin{matrix} 1 - 1 & 2 - 2 3 + 1 & 4 - 7 \end{matrix}] = [\begin{matrix} 0 & 0 4 & - 3 \end{matrix}]$
(ii) $[\begin{matrix} 2 & 3 & 4 4 & 6 & 7 \end{matrix}] - [\begin{matrix} 0 & 2 & 3 6 & - 1 & 0 \end{matrix}] = [\begin{matrix} 2 - 0 & 3 - 2 & 4 - 3 4 - 6 & 6 + 1 & 7 + 0 \end{matrix}] = [\begin{matrix} 2 & 1 & 1 - 2 & 7 & 7 \end{matrix}]$
(iii) $[\begin{matrix} 0 & 1 & 2 4 & 6 & 7 \end{matrix}] + [\begin{matrix} 3 & 4 6 & 8 \end{matrix}]$

single matrix is not possible beacuse they are of different orders

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Similar questions

Show that $(i) [\begin{matrix} 5 & - 1 6 & 7 \end{matrix}] [\begin{matrix} 2 & 1 3 & 4 \end{matrix}] \neq [\begin{matrix} 2 & 1 3 & 4 \end{matrix}] [\begin{matrix} 5 & - 1 6 & 7 \end{matrix}]$

$(i i) ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 0 & 1 & 0 1 & 1 & 0 \end{matrix} ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ \begin{matrix} - 1 & 1 & 0 0 & - 1 & 1 2 & 3 & 4 \end{matrix} ⎤ ⎥ ⎦ \neq ⎡ ⎢ ⎣ \begin{matrix} - 1 & 1 & 0 0 & - 1 & 1 2 & 3 & 4 \end{matrix} ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 0 & 1 & 0 1 & 1 & 0 \end{matrix} ⎤ ⎥ ⎦$

Let $A = [\begin{matrix} 2 & 1 0 & - 2 \end{matrix}], B = [\begin{matrix} 4 & 1 - 3 & - 2 \end{matrix}]$ and $C = [\begin{matrix} - 3 & 2 - 1 & 4 \end{matrix}]$ Find: $A^{2} + A C - 5 B$

Given A $= [\begin{matrix} 0 & 4 & 6 3 & 0 & - 1 \end{matrix}]$
$B = ⎡ ⎢ ⎣ \begin{matrix} 0 & 1 - 1 & 2 - 5 & - 6 \end{matrix} ⎤ ⎥ ⎦$
is the following possible:
(i) AB (ii) BA (iii) $A^{2}$

Compute the following:
$(i) [\begin{matrix} a & b - b & a \end{matrix}] + [\begin{matrix} a & b b & a \end{matrix}]$

$(i i) [\begin{matrix} a^{2} + b^{2} & b^{2} + c^{2} a^{2} + c^{2} & a^{2} + b^{2} \end{matrix}] + [\begin{matrix} 2 a b & 2 b c - 2 a c & - 2 a b \end{matrix}]$

$(i i i) ⎡ ⎢ ⎣ \begin{matrix} - 1 & 4 & - 6 8 & 5 & 16 2 & 8 & 5 \end{matrix} ⎤ ⎥ ⎦ + ⎡ ⎢ ⎣ \begin{matrix} 12 & 7 & 6 8 & 0 & 5 3 & 2 & 4 \end{matrix} ⎤ ⎥ ⎦$

$(i v) [\begin{matrix} c o s^{2} x & s i n^{2} x s i n^{2} x & c o s^{2} x \end{matrix}] + [\begin{matrix} s i n^{2} x & c o s^{2} x c o s^{2} x & s i n^{2} x \end{matrix}]$

Express the following matrices as the sum of a symmetric and a skew-symmetric matrices
$(i) [\begin{matrix} 3 & 5 1 & - 1 \end{matrix}]$

$(i i) ⎡ ⎢ ⎣ \begin{matrix} 6 & - 2 & 2 - 2 & 3 & - 1 2 & - 1 & 3 \end{matrix} ⎤ ⎥ ⎦$

$(i i i) ⎡ ⎢ ⎣ \begin{matrix} 3 & 3 & - 1 - 2 & - 2 & 1 - 4 & - 5 & 2 \end{matrix} ⎤ ⎥ ⎦$

$(i v) [\begin{matrix} 1 & 5 - 1 & 2 \end{matrix}]$

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Wherever possible, write each of the following as a single matrix (i)[1234]+[−1−21−7] (ii)[234467]−[0236−10] (iii)[012467]+[3468]

(i)[1234]+[−1−21−7]=[1−12−23+14−7]=[004−3] (ii)[234467]−[0236−10]=[2−03−24−34−66+17+0]=[211−277]​​​​​​​ (iii)[012467]+[3468]​​​​​​​ single matrix is not possible beacuse they are of different orders