If A - - 23 1 53- 13 23 43- 73 2 23 - and B - - 25 35 1- 15 25 45- 75 65 25 - then compute 3A - 5B-

Name: NCERT - Grade 12 - Mathematics - Matrices - Q34
Uploaded: 2022-07-04T10:36:42+05:30
Description: Given : nbsp;A = [ 23 amp;1 amp;53; 13 amp;23 amp;43; 73 amp;2 amp;23 ] and B = nbsp;[ 25 amp;35 amp;1; 15 amp;25 amp;45; 75 amp ...

Given : nbsp;A = [ 23 amp;1 amp;53; 13 amp;23 amp;43; 73 amp;2 amp;23 ] and B = nbsp;[ 25 amp;35 amp;1; 15 amp;25 amp;45; 75 amp ...

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Byju's Answer

Standard IX

Mathematics

Addition of Polynomials

If A = [ 23 1...

Question

If $A = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} \frac{2}{3} & 1 & \frac{5}{3} \frac{1}{3} & \frac{2}{3} & \frac{4}{3} \frac{7}{3} & 2 & \frac{2}{3} \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦$ and $B = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} \frac{2}{5} & \frac{3}{5} & 1 \frac{1}{5} & \frac{2}{5} & \frac{4}{5} \frac{7}{5} & \frac{6}{5} & \frac{2}{5} \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦,$ then compute $3 A - 5 B$ .

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Solution

Given : $A = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} \frac{2}{3} & 1 & \frac{5}{3} \frac{1}{3} & \frac{2}{3} & \frac{4}{3} \frac{7}{3} & 2 & \frac{2}{3} \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦$ and $B = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} \frac{2}{5} & \frac{3}{5} & 1 \frac{1}{5} & \frac{2}{5} & \frac{4}{5} \frac{7}{5} & \frac{6}{5} & \frac{2}{5} \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦$
Now, $3 A - 5 B = 3 ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} \frac{2}{3} & 1 & \frac{5}{3} \frac{1}{3} & \frac{2}{3} & \frac{4}{3} \frac{7}{3} & 2 & \frac{2}{3} \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ - 5 ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} \frac{2}{5} & \frac{3}{5} & 1 \frac{1}{5} & \frac{2}{5} & \frac{4}{5} \frac{7}{5} & \frac{6}{5} & \frac{2}{5} \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦$
$= ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} \frac{2}{3} \times 3 & 1 \times 3 & \frac{5}{3} \times 3 \frac{1}{3} \times 3 & \frac{2}{3} \times 3 & \frac{4}{3} \times 3 \frac{7}{3} \times 3 & 2 \times 3 & \frac{2}{3} \times 3 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ - ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} \frac{2}{5} \times 5 & \frac{3}{5} \times 5 & 1 \times 5 \frac{1}{5} \times 5 & \frac{2}{5} \times 5 & \frac{4}{5} \times 5 \frac{7}{5} \times 5 & \frac{6}{5} \times 5 & \frac{2}{5} \times 5 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦$
$= ⎡ ⎢ ⎣ \begin{matrix} 2 & 3 & 5 1 & 2 & 4 7 & 6 & 2 \end{matrix} ⎤ ⎥ ⎦ - ⎡ ⎢ ⎣ \begin{matrix} 2 & 3 & 5 1 & 2 & 4 7 & 6 & 2 \end{matrix} ⎤ ⎥ ⎦$
$= ⎡ ⎢ ⎣ \begin{matrix} 2 - 2 & 3 - 3 & 5 - 5 1 - 1 & 2 - 2 & 4 - 4 7 - 7 & 6 - 6 & 2 - 2 \end{matrix} ⎤ ⎥ ⎦$
$= ⎡ ⎢ ⎣ \begin{matrix} 0 & 0 & 0 0 & 0 & 0 0 & 0 & 0 \end{matrix} ⎤ ⎥ ⎦$

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Similar questions

Q. If

A = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} \frac{2}{3} \frac{1}{3} \frac{7}{3} \end{matrix} \begin{matrix} 1 \frac{2}{3} 2 \end{matrix} \begin{matrix} \frac{5}{3} \frac{4}{3} \frac{2}{3} \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

and

B = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} \frac{2}{5} \frac{1}{5} \frac{7}{5} \end{matrix} \begin{matrix} \frac{3}{5} \frac{2}{5} \frac{6}{5} \end{matrix} \begin{matrix} 1 \frac{4}{5} \frac{2}{5} \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

, then compute

3 A - 5 B

Q. Solve:

\frac{2}{5} + \frac{3}{5^{2}} + \frac{2}{5^{3}} + \frac{3}{5^{4}} + \frac{2}{5^{5}} + \frac{3}{5^{6}} + . . . . . .

Find the sum of the following series to infinity :

(i) $1 - \frac{1}{3} + \frac{1}{3^{2}} - \frac{1}{3^{3}} + \frac{1}{3^{4}} + . . . . \infty$

(ii) $8 + 4 \sqrt{2} + 4 + . . . . \infty$

(iii) $\frac{2}{5} + \frac{3}{5^{2}} + \frac{2}{5^{3}} + \frac{3}{5^{4}} + . . . . . \infty$ .

(iv) 10 - 9 + 8.1 - 7.29 + ...... $\infty$

(v) $\frac{1}{3} + \frac{1}{5^{2}} + \frac{1}{3^{3}} + \frac{1}{5^{4}} + \frac{1}{3^{5}} + \frac{1}{5^{6}} + . . . . . \infty$

Q. Tick (✓) the correct answer
What should be subtracted from

\frac{- 5}{3} to get \frac{5}{6} ?

(a)

\frac{5}{2}

(b)

\frac{3}{2}

(c)

\frac{5}{4}

(d)

\frac{- 5}{2}

Q. If

\frac{25}{k} = 1^{2} - \frac{2^{2}}{5} + \frac{3^{2}}{5^{2}} - \frac{4^{2}}{5^{3}} + \frac{5^{2}}{5^{4}} - \frac{6^{2}}{5^{2}} + . . . . . . \infty

, then find the value of

k

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Addition of Polynomials

Standard IX Mathematics

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If A=⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣2315313234373223⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦ and B=⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣25351152545756525⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦, then compute 3A−5B.